From 2e76462fd74e0d1dd7a32347cc6b6795bac512b2 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Tue, 24 May 2022 19:12:13 +0200
Subject: [PATCH 01/62] created the circuit sandbox widget

---
 .../MiniComposer/CircuitSandboxWidget.vue     | 229 ++++++++++++++++++
 .../components/MiniComposer/MatrixView.vue    |   0
 .../MiniComposer/SymbolicNotation.vue         |   0
 frontend/vue/main.ts                          |   2 +
 notebooks/examples/widgets.ipynb              |  22 +-
 5 files changed, 250 insertions(+), 3 deletions(-)
 create mode 100644 frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
 create mode 100644 frontend/vue/components/MiniComposer/MatrixView.vue
 create mode 100644 frontend/vue/components/MiniComposer/SymbolicNotation.vue

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
new file mode 100644
index 000000000..b402a1257
--- /dev/null
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -0,0 +1,229 @@
+<template>
+  <section class="mini-composer">
+    <div
+      ref="configRef"
+      class="mini-composer__config-container"
+    >
+      <slot />
+    </div>
+    <div
+      ref="instructionsRef"
+      class="mini-composer__exercise-text"
+    />
+    <div class="mini-composer__gates">
+      <h1 class="mini-composer__gates__title">
+        Gates
+      </h1>
+      <GatesPool :available-gates="availableGates" />
+    </div>
+    <div class="mini-composer__circuit-section">
+      <h1 class="mini-composer__circuit-section__title">
+        Circuit
+      </h1>
+      <Circuit
+        :circuit-state="circuitState"
+        :auto-measure-gate="autoMeasureGate"
+        :max-lines="circuitState.length"
+      />
+    </div>
+    <div class="mini-composer__lesson">
+      <div>\\sqrt[3]{\\frac xy}</div>
+    </div>
+  </section>
+</template>
+
+<script lang="ts">
+import { ref } from '@vue/reactivity'
+import { Options, Vue, prop } from 'vue-class-component'
+import draggable from 'vuedraggable'
+import Carousel from '../Carousel/Carousel.vue'
+import KetCircuitLine from '../Sketch/KetCircuitLine.vue'
+import AppCta from '../common/AppCta.vue'
+import SolutionStateIndicator, { SolutionState } from '../common/SolutionStateIndicator.vue'
+import GatesPool from './GatesPool.vue'
+import Circuit from './Circuit.vue'
+import { ComposerGate } from './composerTypes'
+import { GateName } from './Gate.vue'
+
+class Props {
+  goal = prop<String>({ default: 'mini-composer-solved', required: true })
+}
+
+@Options({
+  components: {
+    Carousel,
+    KetCircuitLine,
+    Circuit,
+    GatesPool,
+    draggable,
+    AppCta,
+    SolutionStateIndicator
+  }
+})
+export default class CircuitSandboxWidget extends Vue.with(Props) {
+  configRef = ref<HTMLDivElement | null>(null)
+  get configDiv () { return (this.configRef as unknown as HTMLDivElement) }
+  instructionsRef = ref<HTMLDivElement | null>(null)
+  get instructions () { return (this.instructionsRef as unknown as HTMLDivElement) }
+  footerInfoRef = ref<HTMLDivElement | null>(null)
+  get footerInfoDiv () { return (this.footerInfoRef as unknown as HTMLDivElement) }
+  lessonRef = ref<HTMLDivElement | null>(null)
+  get lessonDiv () { return (this.lessonRef as unknown as HTMLDivElement) }
+
+  correctSolution = SolutionState.CORRECT
+
+  autoMeasureGate: boolean = false
+
+  availableGates: ComposerGate[] = []
+
+  circuitState: ComposerGate[][] = [[]]
+
+  lastGateId = 0
+
+  mathjaxRenderer: any | undefined = undefined
+
+  mounted () {
+    const instructionElement = this.configDiv.querySelector('.instructions')
+    const circuitElement = this.configDiv.querySelector('.circuit')
+
+    this.setCircuitConfig(circuitElement as HTMLElement)
+
+    if (instructionElement) {
+      this.instructions.appendChild(instructionElement)
+    } else {
+      this.instructions.remove()
+    }
+  }
+
+  setCircuitConfig (htmlConfigElement: HTMLElement) {
+    this.autoMeasureGate = !!htmlConfigElement.querySelector('.autoMeasureGate')
+
+    const availableGatesElement = htmlConfigElement.querySelector('.availableGates') as HTMLElement
+    this.availableGates = []
+    if (availableGatesElement && availableGatesElement.textContent) {
+      this.availableGates = this.stringToGateNameArray(availableGatesElement.textContent)
+    }
+
+    const initialCircuitElement = Array.from<HTMLElement>(htmlConfigElement.querySelectorAll('.initialCircuit .qubit'))
+    this.circuitState = this.htmlElementsToCircuit(initialCircuitElement)
+  }
+
+  stringToGateNameArray (text: string) : ComposerGate[] {
+    return text.split(' ')
+      .filter(text => text !== '')
+      .map<ComposerGate>((gateText: string) => {
+        if (Object.values(GateName).some(gate => gateText.startsWith(gate))) {
+          const parts = gateText.split('(')
+          const gateName = parts[0]
+          const rotation = parts[1]?.split(')')[0]
+          return { name: gateName as GateName, id: this.lastGateId++, rotation }
+        }
+        return { name: GateName.UNKNOWN, id: this.lastGateId++ }
+      })
+  }
+
+  htmlElementsToCircuit (elements: HTMLElement[]) : ComposerGate[][] {
+    return elements.map((qubitLine: HTMLElement) => {
+      if (qubitLine.textContent === null) {
+        return []
+      }
+      return this.stringToGateNameArray(qubitLine.textContent)
+    })
+  }
+
+  onRestartButton () {
+
+  }
+}
+</script>
+<style scoped lang="scss">
+@import 'carbon-components/scss/globals/scss/typography';
+@import 'carbon-components/scss/globals/scss/layout';
+@import '../../../scss/variables/colors.scss';
+@import '~/../scss/variables/mq.scss';
+
+.mini-composer {
+  display: grid;
+  min-height: 36rem;
+  grid-template-columns: 320px 1fr 160px;
+  grid-template-rows: min-content min-content min-content auto min-content;
+  grid-template-areas:
+    "text text text"
+    "gates lesson lesson"
+    "circuit lesson lesson"
+    "chart lesson lesson"
+    "footer footer footer";
+
+  &__config-container {
+    display: none;
+  }
+
+  &__exercise-text {
+    grid-area: text;
+    border-bottom: 1px solid $border-color;
+
+    ::v-deep(.carousel__selector) {
+      margin-top: 0;
+    }
+  }
+  &__gates {
+    grid-area: gates;
+    border-bottom: 1px solid $border-color;
+    padding: 0 $spacing-05 $spacing-05 $spacing-05;
+    &__title {
+      margin: $spacing-03 0 $spacing-05 0;
+      @include type-style('heading-01');
+    }
+  }
+  &__circuit-section {
+    grid-area: circuit;
+    padding: 0 $spacing-04;
+    &__title {
+      margin-top: $spacing-03;
+      @include type-style('heading-01');
+    }
+    &__qubit-line {
+      position: relative;
+      &__slot-container {
+        display: flex;
+        flex-flow: row;
+
+        position: absolute;
+        top: 0px;
+        height: 100%;
+        width: 100%;
+        align-items: center;
+        padding: 0 $spacing-07;
+      }
+      &__slot {
+        display: flex;
+        flex-flow: row;
+        flex: 1 1 auto;
+        max-width: 100%;
+
+        &__gate {
+          margin-right: $spacing-02;
+          &.sortable-ghost {
+            transition: opacity 0.2s ease-out;
+            opacity: 0.5;
+          }
+        }
+      }
+      &__z-gate {
+        flex: 0 0 auto;
+      }
+    }
+  }
+  &__probability-chart {
+    grid-area: chart;
+    height: 250px;
+    padding: $spacing-07 $spacing-09 $spacing-07 $spacing-05;
+  }
+  &__lesson {
+    grid-area: lesson;
+    border-left: 1px solid $border-color;
+    padding: $spacing-06;
+    margin-bottom: $spacing-10;
+  }
+}
+</style>
diff --git a/frontend/vue/components/MiniComposer/MatrixView.vue b/frontend/vue/components/MiniComposer/MatrixView.vue
new file mode 100644
index 000000000..e69de29bb
diff --git a/frontend/vue/components/MiniComposer/SymbolicNotation.vue b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
new file mode 100644
index 000000000..e69de29bb
diff --git a/frontend/vue/main.ts b/frontend/vue/main.ts
index 59f53d88f..26a9bd317 100644
--- a/frontend/vue/main.ts
+++ b/frontend/vue/main.ts
@@ -10,6 +10,7 @@ import DragAndDropCode from './components/DragAndDropCode/DragAndDropCode.vue'
 import EndUserLicenseAgreementLayout from './components/UserAccount/EndUserLicenseAgreementLayout.vue'
 import Carousel from './components/Carousel/Carousel.vue'
 import MiniComposer from './components/MiniComposer/MiniComposer.vue'
+import CircuitSandboxWidget from './components/MiniComposer/CircuitSandboxWidget.vue'
 import Quiz from './components/Quiz/Quiz.vue'
 import AppCta from './components/common/AppCta.vue'
 import ContentMenu from './components/common/ContentMenu.vue'
@@ -74,6 +75,7 @@ const components: any = {
   UniversalGlossary,
   EmptyPanel,
   MiniComposer,
+  CircuitSandboxWidget,
   Binary,
   BinaryTile,
   SignIn,
diff --git a/notebooks/examples/widgets.ipynb b/notebooks/examples/widgets.ipynb
index 968890223..f47bc6d35 100644
--- a/notebooks/examples/widgets.ipynb
+++ b/notebooks/examples/widgets.ipynb
@@ -7,6 +7,22 @@
     "# Widgets"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## minicomposer\n",
+    "\n",
+    "    q-circuit-sandbox-widget(goal=\"minicomposer\")\n",
+    "        .slide\n",
+    "            .circuit\n",
+    "                .availableGates H X Z\n",
+    "                .initialCircuit\n",
+    "                    .qubit\n",
+    "            .instructions first slide instructions\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -53,13 +69,13 @@
    "cell_type": "code",
    "execution_count": null,
    "metadata": {
-    "grader_function": "grade_ex1a('')",
-    "grader_import": "from qc_grader.challenges.test_challenge import grade_ex1a",
     "goals": [
      {
       "id": "widgets-grader-cell"
      }
-    ]
+    ],
+    "grader_function": "grade_ex1a('')",
+    "grader_import": "from qc_grader.challenges.test_challenge import grade_ex1a"
    },
    "outputs": [],
    "source": [

From 6074e736d7eee7ea4e3f852eef9a28d20ca92ab1 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Fri, 27 May 2022 18:45:19 +0200
Subject: [PATCH 02/62] mathjax working

---
 .../MiniComposer/CircuitSandboxWidget.vue     |   4 +-
 .../MiniComposer/SymbolicNotation.vue         |  54 +++++++
 package-lock.json                             | 133 ++++++++++++++++--
 package.json                                  |   1 +
 4 files changed, 183 insertions(+), 9 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index b402a1257..7f1cdb282 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -27,7 +27,7 @@
       />
     </div>
     <div class="mini-composer__lesson">
-      <div>\\sqrt[3]{\\frac xy}</div>
+      <SymbolicNotation />
     </div>
   </section>
 </template>
@@ -44,6 +44,7 @@ import GatesPool from './GatesPool.vue'
 import Circuit from './Circuit.vue'
 import { ComposerGate } from './composerTypes'
 import { GateName } from './Gate.vue'
+import SymbolicNotation from './SymbolicNotation.vue'
 
 class Props {
   goal = prop<String>({ default: 'mini-composer-solved', required: true })
@@ -57,6 +58,7 @@ class Props {
     GatesPool,
     draggable,
     AppCta,
+    SymbolicNotation,
     SolutionStateIndicator
   }
 })
diff --git a/frontend/vue/components/MiniComposer/SymbolicNotation.vue b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
index e69de29bb..4dab529a2 100644
--- a/frontend/vue/components/MiniComposer/SymbolicNotation.vue
+++ b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
@@ -0,0 +1,54 @@
+<template>
+  <div
+    ref="outputRef"
+    class="symbolic-notation"
+  >
+    <!--VueMathjax :formula="'$$x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a}.$$'" /-->
+  </div>
+</template>
+
+<script lang="ts">
+import { ref } from '@vue/reactivity'
+import { Vue } from 'vue-class-component'
+import 'mathjax-full/es5/tex-chtml.js'
+
+declare global {
+  interface Window {
+    MathJax: any
+  }
+}
+
+export default class SymbolicNotation extends Vue {
+  outputRef = ref<HTMLDivElement | null>(null)
+  get output () { return (this.outputRef as unknown as HTMLDivElement) }
+
+  mounted () {
+    const MathJax = window.MathJax
+    const output = this.output
+
+    MathJax.startup.promise.then(() => {
+      MathJax.texReset()
+      const options = MathJax.getMetricsFor(output)
+      options.display = true
+      MathJax
+        .tex2chtmlPromise('x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a}', options)
+        .then((node: any) => {
+          console.log('NODE: ', node)
+          //
+          //  The promise returns the typeset node, which we add to the output
+          //  Then update the document to include the adjusted CSS for the
+          //    content of the new equation.
+          //
+          output.appendChild(node)
+          MathJax.startup.document.clear()
+          MathJax.startup.document.updateDocument()
+        }).catch((err: Error) => {
+          //
+          //  If there was an error, put the message into the output instead
+          //
+          output.appendChild(document.createElement('pre')).appendChild(document.createTextNode(err.message))
+        })
+    })
+  }
+}
+</script>
diff --git a/package-lock.json b/package-lock.json
index e0e9416c8..b1e280d9d 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -35,6 +35,7 @@
         "lit-element": "^2.5.1",
         "lodash": "^4.17.21",
         "markdown-it": "^12.2.0",
+        "mathjax-full": "^3.2.1",
         "mongodb": "4.3.1",
         "nanoid": "^3.3.4",
         "patch-package": "^6.4.7",
@@ -1936,6 +1937,11 @@
         "node": ">= 12"
       }
     },
+    "node_modules/@mathigon/studio/node_modules/mathjax": {
+      "version": "3.1.2",
+      "resolved": "https://registry.npmjs.org/mathjax/-/mathjax-3.1.2.tgz",
+      "integrity": "sha512-BojKspBv4nNWzO1wC6VEI+g9gHDOhkaGHGgLxXkasdU4pwjdO5AXD5M/wcLPkXYPjZ/N+6sU8rjQTlyvN2cWiQ=="
+    },
     "node_modules/@mathigon/studio/node_modules/node-fetch": {
       "version": "2.6.6",
       "resolved": "https://registry.npmjs.org/node-fetch/-/node-fetch-2.6.6.tgz",
@@ -10596,6 +10602,14 @@
         "node": ">=10.13.0"
       }
     },
+    "node_modules/esm": {
+      "version": "3.2.25",
+      "resolved": "https://registry.npmjs.org/esm/-/esm-3.2.25.tgz",
+      "integrity": "sha512-U1suiZ2oDVWv4zPO56S0NcR5QriEahGtdN2OR6FiOG4WJvcjBVFB0qI4+eKoWFH483PKGuLuu6V8Z4T5g63UVA==",
+      "engines": {
+        "node": ">=6"
+      }
+    },
     "node_modules/espree": {
       "version": "9.3.2",
       "resolved": "https://registry.npmjs.org/espree/-/espree-9.3.2.tgz",
@@ -15491,10 +15505,16 @@
         "node": ">= 10"
       }
     },
-    "node_modules/mathjax": {
-      "version": "3.1.2",
-      "resolved": "https://registry.npmjs.org/mathjax/-/mathjax-3.1.2.tgz",
-      "integrity": "sha512-BojKspBv4nNWzO1wC6VEI+g9gHDOhkaGHGgLxXkasdU4pwjdO5AXD5M/wcLPkXYPjZ/N+6sU8rjQTlyvN2cWiQ=="
+    "node_modules/mathjax-full": {
+      "version": "3.2.1",
+      "resolved": "https://registry.npmjs.org/mathjax-full/-/mathjax-full-3.2.1.tgz",
+      "integrity": "sha512-aUz9o16MGZdeiIBwZjAfUBTiJb7LRqzZEl1YOZ8zQMGYIyh1/nxRebxKxjDe9L+xcZCr2OHdzoFBMcd6VnLv9Q==",
+      "dependencies": {
+        "esm": "^3.2.25",
+        "mhchemparser": "^4.1.0",
+        "mj-context-menu": "^0.6.1",
+        "speech-rule-engine": "^4.0.6"
+      }
     },
     "node_modules/md5-file": {
       "version": "5.0.0",
@@ -15685,6 +15705,11 @@
         "node": ">= 0.6"
       }
     },
+    "node_modules/mhchemparser": {
+      "version": "4.1.1",
+      "resolved": "https://registry.npmjs.org/mhchemparser/-/mhchemparser-4.1.1.tgz",
+      "integrity": "sha512-R75CUN6O6e1t8bgailrF1qPq+HhVeFTM3XQ0uzI+mXTybmphy3b6h4NbLOYhemViQ3lUs+6CKRkC3Ws1TlYREA=="
+    },
     "node_modules/microevent.ts": {
       "version": "0.1.1",
       "resolved": "https://registry.npmjs.org/microevent.ts/-/microevent.ts-0.1.1.tgz",
@@ -16064,6 +16089,11 @@
         "node": ">=0.10.0"
       }
     },
+    "node_modules/mj-context-menu": {
+      "version": "0.6.1",
+      "resolved": "https://registry.npmjs.org/mj-context-menu/-/mj-context-menu-0.6.1.tgz",
+      "integrity": "sha512-7NO5s6n10TIV96d4g2uDpG7ZDpIhMh0QNfGdJw/W47JswFcosz457wqz/b5sAKvl12sxINGFCn80NZHKwxQEXA=="
+    },
     "node_modules/mkdirp": {
       "version": "0.5.6",
       "resolved": "https://registry.npmjs.org/mkdirp/-/mkdirp-0.5.6.tgz",
@@ -23084,6 +23114,27 @@
         "wbuf": "^1.7.3"
       }
     },
+    "node_modules/speech-rule-engine": {
+      "version": "4.0.6",
+      "resolved": "https://registry.npmjs.org/speech-rule-engine/-/speech-rule-engine-4.0.6.tgz",
+      "integrity": "sha512-Hqa4ywf7d3lX2YsnnE8BeEdqFyaTwPSyyVhVGWZlQw4XVh0NCijyVsMZD3I9HsG5JBuDXyRaMVVNZcGJlKbZxA==",
+      "dependencies": {
+        "commander": "9.2.0",
+        "wicked-good-xpath": "1.3.0",
+        "xmldom-sre": "0.1.31"
+      },
+      "bin": {
+        "sre": "bin/sre"
+      }
+    },
+    "node_modules/speech-rule-engine/node_modules/commander": {
+      "version": "9.2.0",
+      "resolved": "https://registry.npmjs.org/commander/-/commander-9.2.0.tgz",
+      "integrity": "sha512-e2i4wANQiSXgnrBlIatyHtP1odfUp0BbV5Y5nEGbxtIrStkEOAAzCUirvLBNXHLr7kwLvJl6V+4V3XV9x7Wd9w==",
+      "engines": {
+        "node": "^12.20.0 || >=14"
+      }
+    },
     "node_modules/split": {
       "version": "0.3.3",
       "resolved": "https://registry.npmjs.org/split/-/split-0.3.3.tgz",
@@ -27349,6 +27400,11 @@
       "integrity": "sha1-2e8H3Od7mQK4o6j6SzHD4/fm6Ho=",
       "dev": true
     },
+    "node_modules/wicked-good-xpath": {
+      "version": "1.3.0",
+      "resolved": "https://registry.npmjs.org/wicked-good-xpath/-/wicked-good-xpath-1.3.0.tgz",
+      "integrity": "sha1-gbDpXoZQ5JyUsiKY//hoa1VTz2w="
+    },
     "node_modules/wide-align": {
       "version": "1.1.5",
       "resolved": "https://registry.npmjs.org/wide-align/-/wide-align-1.1.5.tgz",
@@ -27545,6 +27601,14 @@
       "resolved": "https://registry.npmjs.org/xmlchars/-/xmlchars-2.2.0.tgz",
       "integrity": "sha512-JZnDKK8B0RCDw84FNdDAIpZK+JuJw+s7Lz8nksI7SIuU3UXJJslUthsi+uWBUYOwPFwW7W7PRLRfUKpxjtjFCw=="
     },
+    "node_modules/xmldom-sre": {
+      "version": "0.1.31",
+      "resolved": "https://registry.npmjs.org/xmldom-sre/-/xmldom-sre-0.1.31.tgz",
+      "integrity": "sha512-f9s+fUkX04BxQf+7mMWAp5zk61pciie+fFLC9hX9UVvCeJQfNHRHXpeo5MPcR0EUf57PYLdt+ZO4f3Ipk2oZUw==",
+      "engines": {
+        "node": ">=0.1"
+      }
+    },
     "node_modules/xss": {
       "version": "1.0.10",
       "resolved": "https://registry.npmjs.org/xss/-/xss-1.0.10.tgz",
@@ -29565,6 +29629,11 @@
           "resolved": "https://registry.npmjs.org/marked/-/marked-4.0.8.tgz",
           "integrity": "sha512-dkpJMIlJpc833hbjjg8jraw1t51e/eKDoG8TFOgc5O0Z77zaYKigYekTDop5AplRoKFGIaoazhYEhGkMtU3IeA=="
         },
+        "mathjax": {
+          "version": "3.1.2",
+          "resolved": "https://registry.npmjs.org/mathjax/-/mathjax-3.1.2.tgz",
+          "integrity": "sha512-BojKspBv4nNWzO1wC6VEI+g9gHDOhkaGHGgLxXkasdU4pwjdO5AXD5M/wcLPkXYPjZ/N+6sU8rjQTlyvN2cWiQ=="
+        },
         "node-fetch": {
           "version": "2.6.6",
           "resolved": "https://registry.npmjs.org/node-fetch/-/node-fetch-2.6.6.tgz",
@@ -36359,6 +36428,11 @@
       "integrity": "sha512-mQ+suqKJVyeuwGYHAdjMFqjCyfl8+Ldnxuyp3ldiMBFKkvytrXUZWaiPCEav8qDHKty44bD+qV1IP4T+w+xXRA==",
       "dev": true
     },
+    "esm": {
+      "version": "3.2.25",
+      "resolved": "https://registry.npmjs.org/esm/-/esm-3.2.25.tgz",
+      "integrity": "sha512-U1suiZ2oDVWv4zPO56S0NcR5QriEahGtdN2OR6FiOG4WJvcjBVFB0qI4+eKoWFH483PKGuLuu6V8Z4T5g63UVA=="
+    },
     "espree": {
       "version": "9.3.2",
       "resolved": "https://registry.npmjs.org/espree/-/espree-9.3.2.tgz",
@@ -40181,10 +40255,16 @@
       "resolved": "https://registry.npmjs.org/marked/-/marked-2.1.3.tgz",
       "integrity": "sha512-/Q+7MGzaETqifOMWYEA7HVMaZb4XbcRfaOzcSsHZEith83KGlvaSG33u0SKu89Mj5h+T8V2hM+8O45Qc5XTgwA=="
     },
-    "mathjax": {
-      "version": "3.1.2",
-      "resolved": "https://registry.npmjs.org/mathjax/-/mathjax-3.1.2.tgz",
-      "integrity": "sha512-BojKspBv4nNWzO1wC6VEI+g9gHDOhkaGHGgLxXkasdU4pwjdO5AXD5M/wcLPkXYPjZ/N+6sU8rjQTlyvN2cWiQ=="
+    "mathjax-full": {
+      "version": "3.2.1",
+      "resolved": "https://registry.npmjs.org/mathjax-full/-/mathjax-full-3.2.1.tgz",
+      "integrity": "sha512-aUz9o16MGZdeiIBwZjAfUBTiJb7LRqzZEl1YOZ8zQMGYIyh1/nxRebxKxjDe9L+xcZCr2OHdzoFBMcd6VnLv9Q==",
+      "requires": {
+        "esm": "^3.2.25",
+        "mhchemparser": "^4.1.0",
+        "mj-context-menu": "^0.6.1",
+        "speech-rule-engine": "^4.0.6"
+      }
     },
     "md5-file": {
       "version": "5.0.0",
@@ -40340,6 +40420,11 @@
       "resolved": "https://registry.npmjs.org/methods/-/methods-1.1.2.tgz",
       "integrity": "sha1-VSmk1nZUE07cxSZmVoNbD4Ua/O4="
     },
+    "mhchemparser": {
+      "version": "4.1.1",
+      "resolved": "https://registry.npmjs.org/mhchemparser/-/mhchemparser-4.1.1.tgz",
+      "integrity": "sha512-R75CUN6O6e1t8bgailrF1qPq+HhVeFTM3XQ0uzI+mXTybmphy3b6h4NbLOYhemViQ3lUs+6CKRkC3Ws1TlYREA=="
+    },
     "microevent.ts": {
       "version": "0.1.1",
       "resolved": "https://registry.npmjs.org/microevent.ts/-/microevent.ts-0.1.1.tgz",
@@ -40657,6 +40742,11 @@
         "is-extendable": "^1.0.1"
       }
     },
+    "mj-context-menu": {
+      "version": "0.6.1",
+      "resolved": "https://registry.npmjs.org/mj-context-menu/-/mj-context-menu-0.6.1.tgz",
+      "integrity": "sha512-7NO5s6n10TIV96d4g2uDpG7ZDpIhMh0QNfGdJw/W47JswFcosz457wqz/b5sAKvl12sxINGFCn80NZHKwxQEXA=="
+    },
     "mkdirp": {
       "version": "0.5.6",
       "resolved": "https://registry.npmjs.org/mkdirp/-/mkdirp-0.5.6.tgz",
@@ -46277,6 +46367,23 @@
         "wbuf": "^1.7.3"
       }
     },
+    "speech-rule-engine": {
+      "version": "4.0.6",
+      "resolved": "https://registry.npmjs.org/speech-rule-engine/-/speech-rule-engine-4.0.6.tgz",
+      "integrity": "sha512-Hqa4ywf7d3lX2YsnnE8BeEdqFyaTwPSyyVhVGWZlQw4XVh0NCijyVsMZD3I9HsG5JBuDXyRaMVVNZcGJlKbZxA==",
+      "requires": {
+        "commander": "9.2.0",
+        "wicked-good-xpath": "1.3.0",
+        "xmldom-sre": "0.1.31"
+      },
+      "dependencies": {
+        "commander": {
+          "version": "9.2.0",
+          "resolved": "https://registry.npmjs.org/commander/-/commander-9.2.0.tgz",
+          "integrity": "sha512-e2i4wANQiSXgnrBlIatyHtP1odfUp0BbV5Y5nEGbxtIrStkEOAAzCUirvLBNXHLr7kwLvJl6V+4V3XV9x7Wd9w=="
+        }
+      }
+    },
     "split": {
       "version": "0.3.3",
       "resolved": "https://registry.npmjs.org/split/-/split-0.3.3.tgz",
@@ -49729,6 +49836,11 @@
       "integrity": "sha1-2e8H3Od7mQK4o6j6SzHD4/fm6Ho=",
       "dev": true
     },
+    "wicked-good-xpath": {
+      "version": "1.3.0",
+      "resolved": "https://registry.npmjs.org/wicked-good-xpath/-/wicked-good-xpath-1.3.0.tgz",
+      "integrity": "sha1-gbDpXoZQ5JyUsiKY//hoa1VTz2w="
+    },
     "wide-align": {
       "version": "1.1.5",
       "resolved": "https://registry.npmjs.org/wide-align/-/wide-align-1.1.5.tgz",
@@ -49877,6 +49989,11 @@
       "resolved": "https://registry.npmjs.org/xmlchars/-/xmlchars-2.2.0.tgz",
       "integrity": "sha512-JZnDKK8B0RCDw84FNdDAIpZK+JuJw+s7Lz8nksI7SIuU3UXJJslUthsi+uWBUYOwPFwW7W7PRLRfUKpxjtjFCw=="
     },
+    "xmldom-sre": {
+      "version": "0.1.31",
+      "resolved": "https://registry.npmjs.org/xmldom-sre/-/xmldom-sre-0.1.31.tgz",
+      "integrity": "sha512-f9s+fUkX04BxQf+7mMWAp5zk61pciie+fFLC9hX9UVvCeJQfNHRHXpeo5MPcR0EUf57PYLdt+ZO4f3Ipk2oZUw=="
+    },
     "xss": {
       "version": "1.0.10",
       "resolved": "https://registry.npmjs.org/xss/-/xss-1.0.10.tgz",
diff --git a/package.json b/package.json
index fea7f2eb5..f7b16fd02 100644
--- a/package.json
+++ b/package.json
@@ -75,6 +75,7 @@
     "lit-element": "^2.5.1",
     "lodash": "^4.17.21",
     "markdown-it": "^12.2.0",
+    "mathjax-full": "^3.2.1",
     "mongodb": "4.3.1",
     "nanoid": "^3.3.4",
     "patch-package": "^6.4.7",

From fc4b6453004b6555d7d5442f65330de8e8abc012 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Thu, 2 Jun 2022 16:47:16 +0200
Subject: [PATCH 03/62] symbolic notation working

---
 .../vue/components/MiniComposer/Circuit.vue   |   2 +-
 .../MiniComposer/CircuitSandboxWidget.vue     |  89 +++++--
 frontend/vue/components/MiniComposer/Gate.vue |  20 +-
 .../vue/components/MiniComposer/GatesPool.vue |   3 +-
 .../components/MiniComposer/MiniComposer.vue  |   8 +-
 .../MiniComposer/ProbablityChart.vue          |   6 +-
 .../vue/components/MiniComposer/QubitLine.vue |   3 +-
 .../MiniComposer/SymbolicNotation.vue         |  46 ++--
 .../components/MiniComposer/composerTypes.ts  |  12 +-
 .../vue/components/MiniComposer/gateUtils.ts  | 241 ++++++++++++++++++
 notebooks/examples/widgets.ipynb              |   2 +-
 package-lock.json                             | 121 ++++++++-
 package.json                                  |   1 +
 13 files changed, 480 insertions(+), 74 deletions(-)
 create mode 100644 frontend/vue/components/MiniComposer/gateUtils.ts

diff --git a/frontend/vue/components/MiniComposer/Circuit.vue b/frontend/vue/components/MiniComposer/Circuit.vue
index fdd73df6a..745878f19 100644
--- a/frontend/vue/components/MiniComposer/Circuit.vue
+++ b/frontend/vue/components/MiniComposer/Circuit.vue
@@ -21,9 +21,9 @@
 
 <script lang="ts">
 import { Options, Vue, prop } from 'vue-class-component'
-import { GateName } from './Gate.vue'
 import QubitLine from './QubitLine.vue'
 import { ComposerGate } from './composerTypes'
+import { GateName } from './gateUtils'
 
 class Props {
   name = prop<String>({ default: GateName.H, required: true })
diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index 7f1cdb282..a936dde7e 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -26,8 +26,25 @@
         :max-lines="circuitState.length"
       />
     </div>
-    <div class="mini-composer__lesson">
-      <SymbolicNotation />
+    <div class="mini-composer__state-views">
+      <section class="mini-composer__state-views__view">
+        <h1 class="mini-composer__state-views__view__title">
+          Matrix
+        </h1>
+        <SymbolicNotation
+          class="mini-composer__state-views__view__area"
+          :tex="matrixTex"
+        />
+      </section>
+      <section class="mini-composer__state-views__view">
+        <h1 class="mini-composer__state-views__view__title">
+          State Vector
+        </h1>
+        <SymbolicNotation
+          class="mini-composer__state-views__view__area"
+          :tex="stateVectorTex"
+        />
+      </section>
     </div>
   </section>
 </template>
@@ -42,8 +59,8 @@ import AppCta from '../common/AppCta.vue'
 import SolutionStateIndicator, { SolutionState } from '../common/SolutionStateIndicator.vue'
 import GatesPool from './GatesPool.vue'
 import Circuit from './Circuit.vue'
-import { ComposerGate } from './composerTypes'
-import { GateName } from './Gate.vue'
+import { ComposerGate, gateMatrix } from './composerTypes'
+import { GateName, IdentityState, StateMatrixToTexMatrix, StateMatrixToTexKetNotation } from './gateUtils'
 import SymbolicNotation from './SymbolicNotation.vue'
 
 class Props {
@@ -82,7 +99,21 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
 
   lastGateId = 0
 
-  mathjaxRenderer: any | undefined = undefined
+  get matrixState () {
+    return this.circuitState[0].reduce((prev, current) => {
+      return gateMatrix(current).apply(prev)
+    }, IdentityState())
+  }
+
+  get matrixTex () {
+    return StateMatrixToTexMatrix(this.matrixState)
+  }
+
+  get stateVectorTex () {
+    return StateMatrixToTexKetNotation(this.matrixState)
+  }
+  // stateVectorTex = 'x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a}'
+  // stateVectorTex = '({\\sqrt{1} \\over 4} + {\\sqrt{1} \\over 4} + {\\sqrt{1} \\over 4} |0\\rangle) + ({\\sqrt{1} \\over 4} + {\\sqrt{1} \\over 4} + {\\sqrt{1} \\over 4}|1\\rangle)'
 
   mounted () {
     const instructionElement = this.configDiv.querySelector('.instructions')
@@ -146,15 +177,12 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
 
 .mini-composer {
   display: grid;
-  min-height: 36rem;
-  grid-template-columns: 320px 1fr 160px;
-  grid-template-rows: min-content min-content min-content auto min-content;
+  grid-template-columns: 20rem 1fr;
+  grid-template-rows: min-content min-content 1fr;
   grid-template-areas:
-    "text text text"
-    "gates lesson lesson"
-    "circuit lesson lesson"
-    "chart lesson lesson"
-    "footer footer footer";
+    "text text"
+    "gates lesson"
+    "circuit lesson";
 
   &__config-container {
     display: none;
@@ -171,7 +199,7 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   &__gates {
     grid-area: gates;
     border-bottom: 1px solid $border-color;
-    padding: 0 $spacing-05 $spacing-05 $spacing-05;
+    padding: $spacing-05;
     &__title {
       margin: $spacing-03 0 $spacing-05 0;
       @include type-style('heading-01');
@@ -179,7 +207,7 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   }
   &__circuit-section {
     grid-area: circuit;
-    padding: 0 $spacing-04;
+    padding: $spacing-05;
     &__title {
       margin-top: $spacing-03;
       @include type-style('heading-01');
@@ -216,16 +244,31 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
       }
     }
   }
-  &__probability-chart {
-    grid-area: chart;
-    height: 250px;
-    padding: $spacing-07 $spacing-09 $spacing-07 $spacing-05;
-  }
-  &__lesson {
+  &__state-views {
     grid-area: lesson;
+    display: flex;
+    flex-direction: column;
+    gap: $spacing-05;
     border-left: 1px solid $border-color;
-    padding: $spacing-06;
-    margin-bottom: $spacing-10;
+    padding: $spacing-05;
+
+    &__view {
+      &__title {
+        @include type-style('heading-01');
+        margin-top: $spacing-03;
+      }
+      &__area {
+        display: flex;
+        flex-direction: column;
+        align-items: center;
+        justify-content: center;
+
+        height: 9rem;
+        width: 100%;
+        border: 2px solid $border-color;
+        background-color: $background-color-white;
+      }
+    }
   }
 }
 </style>
diff --git a/frontend/vue/components/MiniComposer/Gate.vue b/frontend/vue/components/MiniComposer/Gate.vue
index 4d9e6af54..c814a716a 100644
--- a/frontend/vue/components/MiniComposer/Gate.vue
+++ b/frontend/vue/components/MiniComposer/Gate.vue
@@ -9,6 +9,12 @@
     <div v-if="name === gateName.Z" class="gate__symbol gate__symbol_text">
       Z
     </div>
+    <div v-if="name === gateName.Y" class="gate__symbol gate__symbol_text">
+      Y
+    </div>
+    <div v-if="name === gateName.T" class="gate__symbol gate__symbol_text">
+      T
+    </div>
     <div v-if="isRotationGate()" class="gate__symbol gate__symbol_text">
       {{ name }}
       <div v-if="rotation" class="gate__symbol__rotation">
@@ -26,17 +32,7 @@ import { Options, Vue, prop } from 'vue-class-component'
 import MeasureZ from './GatesSVG/MeasureZ.vue'
 import Theta from './GatesSVG/Theta.vue'
 import Phi from './GatesSVG/Phi.vue'
-
-export enum GateName {
-  UNKNOWN = 'UNKNOWN',
-  H = 'H',
-  Z = 'Z',
-  X = 'X',
-  RX = 'RX',
-  RZ = 'RZ',
-  RY = 'RY',
-  MEASURE_Z = 'Measure'
-}
+import { GateName } from './gateUtils'
 
 class Props {
   name = prop<String>({ default: GateName.H, required: true })
@@ -51,7 +47,7 @@ class Props {
   }
 })
 export default class Gate extends Vue.with(Props) {
-  gateName = GateName;
+  gateName = GateName
 
   isRotationGate (): Boolean {
     return this.name === GateName.RY || this.name === GateName.RX || this.name === GateName.RZ
diff --git a/frontend/vue/components/MiniComposer/GatesPool.vue b/frontend/vue/components/MiniComposer/GatesPool.vue
index d0dc60d2e..35c548fbb 100644
--- a/frontend/vue/components/MiniComposer/GatesPool.vue
+++ b/frontend/vue/components/MiniComposer/GatesPool.vue
@@ -17,7 +17,8 @@
 import { Options, Vue, prop } from 'vue-class-component'
 import draggable from 'vuedraggable'
 import KetCircuitLine from '../Sketch/KetCircuitLine.vue'
-import Gate, { GateName } from './Gate.vue'
+import Gate from './Gate.vue'
+import { GateName } from './gateUtils'
 
 interface ComposerGate {
   name: GateName
diff --git a/frontend/vue/components/MiniComposer/MiniComposer.vue b/frontend/vue/components/MiniComposer/MiniComposer.vue
index c897ba1c3..bcab3430a 100644
--- a/frontend/vue/components/MiniComposer/MiniComposer.vue
+++ b/frontend/vue/components/MiniComposer/MiniComposer.vue
@@ -76,12 +76,12 @@ import AppCta from '../common/AppCta.vue'
 import SolutionStateIndicator, { SolutionState } from '../common/SolutionStateIndicator.vue'
 import GatesPool from './GatesPool.vue'
 import Circuit from './Circuit.vue'
-import ProbablityChart, { ProbabilityState } from './ProbablityChart.vue'
-import { ExerciseStep, ComposerGate, emptyExerciseStep } from './composerTypes'
-import { GateName } from './Gate.vue'
+import ProbablityChart from './ProbablityChart.vue'
+import { ExerciseStep, ComposerGate, emptyExerciseStep, ProbabilityState } from './composerTypes'
+import { GateName } from './gateUtils'
 
 class Props {
-  goal = prop<String>({ default: 'mini-composer-solved', required: true });
+  goal = prop<String>({ default: 'mini-composer-solved', required: true })
 }
 
 @Options({
diff --git a/frontend/vue/components/MiniComposer/ProbablityChart.vue b/frontend/vue/components/MiniComposer/ProbablityChart.vue
index d1dfaaa86..9fb57f8fc 100644
--- a/frontend/vue/components/MiniComposer/ProbablityChart.vue
+++ b/frontend/vue/components/MiniComposer/ProbablityChart.vue
@@ -35,11 +35,7 @@
 
 <script lang="ts">
 import { Vue, prop } from 'vue-class-component'
-
-export interface ProbabilityState {
-  key: string
-  value: number
-}
+import { ProbabilityState } from './composerTypes'
 
 class Props {
   probabilities = prop<ProbabilityState[]>({
diff --git a/frontend/vue/components/MiniComposer/QubitLine.vue b/frontend/vue/components/MiniComposer/QubitLine.vue
index 3a5f07688..7883c99fe 100644
--- a/frontend/vue/components/MiniComposer/QubitLine.vue
+++ b/frontend/vue/components/MiniComposer/QubitLine.vue
@@ -27,8 +27,9 @@
 import { Options, Vue, prop } from 'vue-class-component'
 import draggable from 'vuedraggable'
 import KetCircuitLine from '../Sketch/KetCircuitLine.vue'
-import Gate, { GateName } from './Gate.vue'
+import Gate from './Gate.vue'
 import { ComposerGate } from './composerTypes'
+import { GateName } from './gateUtils'
 
 class Props {
   name = prop<GateName>({ default: GateName.H, required: true })
diff --git a/frontend/vue/components/MiniComposer/SymbolicNotation.vue b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
index 4dab529a2..8fe1f59c2 100644
--- a/frontend/vue/components/MiniComposer/SymbolicNotation.vue
+++ b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
@@ -2,53 +2,63 @@
   <div
     ref="outputRef"
     class="symbolic-notation"
-  >
-    <!--VueMathjax :formula="'$$x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a}.$$'" /-->
-  </div>
+  />
 </template>
 
 <script lang="ts">
 import { ref } from '@vue/reactivity'
-import { Vue } from 'vue-class-component'
+import { Vue, prop } from 'vue-class-component'
 import 'mathjax-full/es5/tex-chtml.js'
 
+class Props {
+  tex = prop<String>({ default: '', required: true })
+}
+
 declare global {
   interface Window {
     MathJax: any
   }
 }
 
-export default class SymbolicNotation extends Vue {
+export default class SymbolicNotation extends Vue.with(Props) {
   outputRef = ref<HTMLDivElement | null>(null)
   get output () { return (this.outputRef as unknown as HTMLDivElement) }
 
   mounted () {
+    this.renderTex()
+    this.$watch('tex', () => this.renderTex())
+  }
+
+  renderTex () {
     const MathJax = window.MathJax
     const output = this.output
 
     MathJax.startup.promise.then(() => {
       MathJax.texReset()
-      const options = MathJax.getMetricsFor(output)
-      options.display = true
+      const options = {
+        ...MathJax.getMetricsFor(output),
+        ...{ display: true }
+      }
       MathJax
-        .tex2chtmlPromise('x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a}', options)
-        .then((node: any) => {
-          console.log('NODE: ', node)
-          //
-          //  The promise returns the typeset node, which we add to the output
-          //  Then update the document to include the adjusted CSS for the
-          //    content of the new equation.
-          //
+        .tex2chtmlPromise(this.tex, options)
+        .then((node: HTMLElement) => {
+          output.childNodes.forEach((child) => {
+            child.remove()
+          })
           output.appendChild(node)
           MathJax.startup.document.clear()
           MathJax.startup.document.updateDocument()
         }).catch((err: Error) => {
-          //
-          //  If there was an error, put the message into the output instead
-          //
+          // If there was an error, put the message into the output instead
           output.appendChild(document.createElement('pre')).appendChild(document.createTextNode(err.message))
         })
     })
   }
 }
 </script>
+
+<style scoped lang="scss">
+.symbolic-notation {
+  width: 100%;
+}
+</style>
diff --git a/frontend/vue/components/MiniComposer/composerTypes.ts b/frontend/vue/components/MiniComposer/composerTypes.ts
index f0e6cb4c8..f581dbd30 100644
--- a/frontend/vue/components/MiniComposer/composerTypes.ts
+++ b/frontend/vue/components/MiniComposer/composerTypes.ts
@@ -1,5 +1,4 @@
-import { GateName } from './Gate.vue'
-import { ProbabilityState } from './ProbablityChart.vue'
+import { GateName, QuantumGate, gateMap } from './gateUtils'
 
 export interface ComposerGate {
   name: GateName
@@ -7,6 +6,11 @@ export interface ComposerGate {
   id: number
 }
 
+export interface ProbabilityState {
+  key: string
+  value: number
+}
+
 export interface ExerciseStep {
   autoMeasureGate: boolean
   availableGates: ComposerGate[]
@@ -28,3 +32,7 @@ export function emptyExerciseStep (): ExerciseStep {
     isCompleted: false
   }
 }
+
+export function gateMatrix (gate: ComposerGate): QuantumGate {
+  return gateMap[gate.name]
+}
diff --git a/frontend/vue/components/MiniComposer/gateUtils.ts b/frontend/vue/components/MiniComposer/gateUtils.ts
new file mode 100644
index 000000000..2a5b0e689
--- /dev/null
+++ b/frontend/vue/components/MiniComposer/gateUtils.ts
@@ -0,0 +1,241 @@
+// eslint-disable-next-line import/named
+import { multiply, subtract, add } from 'mathjs'
+
+export enum GateName {
+  UNKNOWN = 'UNKNOWN',
+  ID = 'ID',
+  H = 'H',
+  Z = 'Z',
+  X = 'X',
+  Y = 'Y',
+  T = 'T',
+  S = 'S',
+  RX = 'RX',
+  RZ = 'RZ',
+  RY = 'RY',
+  MEASURE_Z = 'Measure'
+}
+
+const mult = multiply
+const sub = subtract
+function neg (m: number[][]) {
+  return multiply(m, -1)
+}
+export interface StateMatrix {
+  A: number[][]
+  B: number[][]
+  C: number[][]
+  D: number[][]
+  m: number
+}
+
+export function IdentityState (): StateMatrix {
+  return {
+    A: [[1, 0], [0, 1]],
+    B: [[0, 0], [0, 0]],
+    C: [[0, 0], [0, 0]],
+    D: [[0, 0], [0, 0]],
+    m: 0
+  }
+}
+
+export interface QuantumGate {
+  apply (state: StateMatrix): StateMatrix
+}
+
+export const Identity: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    return state
+  }
+}
+
+export const XGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K = [[0, 1], [1, 0]]
+    return {
+      A: mult(K, state.A),
+      B: mult(K, state.B),
+      C: mult(K, state.C),
+      D: mult(K, state.D),
+      m: state.m
+    }
+  }
+}
+
+export const YGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K = [[0, -1], [1, 0]]
+
+    return {
+      A: neg(mult(K, state.B)),
+      B: mult(K, state.A),
+      C: neg(mult(K, state.D)),
+      D: mult(K, state.C),
+      m: state.m
+    }
+  }
+}
+
+export const ZGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K = [[1, 0], [0, -1]]
+
+    return {
+      A: mult(K, state.A),
+      B: mult(K, state.B),
+      C: mult(K, state.C),
+      D: mult(K, state.D),
+      m: state.m
+    }
+  }
+}
+
+export const HGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K = [[1, 1], [1, -1]]
+
+    return {
+      A: mult(mult(K, state.C), 2),
+      B: mult(mult(K, state.D), 2),
+      C: mult(K, state.A),
+      D: mult(K, state.B),
+      m: state.m + 1
+    }
+  }
+}
+
+export const SGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K1 = [[1, 0], [0, 0]]
+    const K2 = [[0, 0], [0, 1]]
+
+    return {
+      A: sub(mult(K1, state.A), mult(K2, state.B)),
+      B: add(mult(K2, state.A), mult(K1, state.B)),
+      C: sub(mult(K1, state.C), mult(K2, state.D)),
+      D: add(mult(K1, state.C), mult(K1, state.D)),
+      m: state.m
+    }
+  }
+}
+
+export const TGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K1 = [[2, 0], [0, 0]]
+    const K2 = [[0, 0], [0, 1]]
+
+    const K1_A = mult(K1, state.A)
+    const K1_B = mult(K1, state.B)
+    const K1_C = mult(K1, state.C)
+    const K1_D = mult(K1, state.D)
+    const K2_A = mult(K2, state.A)
+    const K2_B = mult(K2, state.B)
+    const K2_C = mult(K2, state.C)
+    const K2_D = mult(K2, state.D)
+    const K2_C_2 = mult(K2_C, 2)
+    const K2_D_2 = mult(K2_D, 2)
+
+    return {
+      A: sub(add(K1_A, K2_C_2), K2_D_2),
+      B: add(add(K1_B, K2_C_2), K2_D_2),
+      C: add(sub(K2_A, K2_B), K1_C),
+      D: add(add(K2_A, K2_B), K1_D),
+      m: state.m + 1
+    }
+  }
+}
+
+export const gateMap = {
+  [GateName.UNKNOWN]: Identity,
+  [GateName.ID]: Identity,
+  [GateName.MEASURE_Z]: Identity,
+  [GateName.H]: HGate,
+  [GateName.X]: XGate,
+  [GateName.Y]: YGate,
+  [GateName.Z]: ZGate,
+  [GateName.T]: TGate,
+  [GateName.S]: SGate,
+  [GateName.RX]: Identity,
+  [GateName.RY]: Identity,
+  [GateName.RZ]: Identity
+}
+
+function signedString (value: number, symbol: string) {
+  if (value === 0) {
+    return ''
+  }
+
+  const absValue = Math.abs(value)
+  return `${value > 0 ? '+' : '-'}${absValue > 1 ? absValue : ''}${symbol}`
+}
+
+function StateMatrixElementToTex (state: StateMatrix, coords: { x: number, y: number }) {
+  const { x, y } = coords
+  const [a, b, c, d] = [state.A[x][y], state.B[x][y], state.C[x][y], state.D[x][y]]
+  const isZero = (Math.pow(a, 2) + Math.pow(b, 2) + Math.pow(c, 2) + Math.pow(d, 2)) === 0
+
+  if (isZero) {
+    return '0'
+  }
+
+  let tex = ''
+
+  if (a !== 0) {
+    tex = `${tex}${a}`
+  }
+
+  tex = `${tex}${signedString(b, 'i')}${signedString(c, '\\sqrt{2}')}${signedString(d, 'i\\sqrt{2}')}`
+
+  if (tex.startsWith('+')) {
+    tex = tex.substring(1)
+  }
+
+  if (state.m > 0) {
+    tex = `\\frac{${tex}}{${Math.pow(2, state.m)}}`
+  }
+
+  return tex
+}
+
+export function StateMatrixToTexMatrix (state: StateMatrix) {
+  return `
+    \\begin{bmatrix}
+      ${StateMatrixElementToTex(state, { x: 0, y: 0 })} & ${StateMatrixElementToTex(state, { x: 0, y: 1 })}\\\\
+      ${StateMatrixElementToTex(state, { x: 1, y: 0 })} & ${StateMatrixElementToTex(state, { x: 1, y: 1 })}
+    \\end{bmatrix}
+  `
+}
+
+const ZERO_KET = '|0\\rangle'
+const ONE_KET = '|1\\rangle'
+
+export function StateMatrixToTexKetNotation (state: StateMatrix) {
+  const zeroKetValue = StateMatrixElementToTex(state, { x: 0, y: 0 })
+  const oneKetValue = StateMatrixElementToTex(state, { x: 1, y: 0 })
+
+  let zeroKetTex = ''
+  let oneKetTex = ''
+  if (zeroKetValue !== '0') {
+    zeroKetTex = `${zeroKetValue === '1' ? '' : zeroKetValue}${ZERO_KET}`
+  }
+
+  if (oneKetValue !== '0') {
+    oneKetTex = `${oneKetValue === '1' ? '' : oneKetValue}${ONE_KET}`
+  }
+
+  let joinTex = ''
+  if (zeroKetTex && oneKetTex && !oneKetTex.startsWith('-')) {
+    joinTex = '+'
+  }
+
+  return `
+    ${zeroKetTex}${joinTex}${oneKetTex}
+  `
+}
diff --git a/notebooks/examples/widgets.ipynb b/notebooks/examples/widgets.ipynb
index f47bc6d35..8c7a66bfe 100644
--- a/notebooks/examples/widgets.ipynb
+++ b/notebooks/examples/widgets.ipynb
@@ -16,7 +16,7 @@
     "    q-circuit-sandbox-widget(goal=\"minicomposer\")\n",
     "        .slide\n",
     "            .circuit\n",
-    "                .availableGates H X Z\n",
+    "                .availableGates H X Z Y T\n",
     "                .initialCircuit\n",
     "                    .qubit\n",
     "            .instructions first slide instructions\n",
diff --git a/package-lock.json b/package-lock.json
index b1e280d9d..9f34085ed 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -36,6 +36,7 @@
         "lodash": "^4.17.21",
         "markdown-it": "^12.2.0",
         "mathjax-full": "^3.2.1",
+        "mathjs": "^10.6.1",
         "mongodb": "4.3.1",
         "nanoid": "^3.3.4",
         "patch-package": "^6.4.7",
@@ -274,9 +275,9 @@
       }
     },
     "node_modules/@babel/runtime": {
-      "version": "7.17.9",
-      "resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.17.9.tgz",
-      "integrity": "sha512-lSiBBvodq29uShpWGNbgFdKYNiFDo5/HIYsaCEY9ff4sb10x9jizo2+pRrSyF4jKZCXqgzuqBOQKbUm90gQwJg==",
+      "version": "7.18.3",
+      "resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.18.3.tgz",
+      "integrity": "sha512-38Y8f7YUhce/K7RMwTp7m0uCumpv9hZkitCbBClqQIow1qSbCvGkcegKOXpEWCQLfWmevgRiWokZ1GkpfhbZug==",
       "dependencies": {
         "regenerator-runtime": "^0.13.4"
       },
@@ -7120,6 +7121,18 @@
       "resolved": "https://registry.npmjs.org/commondir/-/commondir-1.0.1.tgz",
       "integrity": "sha1-3dgA2gxmEnOTzKWVDqloo6rxJTs="
     },
+    "node_modules/complex.js": {
+      "version": "2.1.1",
+      "resolved": "https://registry.npmjs.org/complex.js/-/complex.js-2.1.1.tgz",
+      "integrity": "sha512-8njCHOTtFFLtegk6zQo0kkVX1rngygb/KQI6z1qZxlFI3scluC+LVTCFbrkWjBv4vvLlbQ9t88IPMC6k95VTTg==",
+      "engines": {
+        "node": "*"
+      },
+      "funding": {
+        "type": "patreon",
+        "url": "https://www.patreon.com/infusion"
+      }
+    },
     "node_modules/component-emitter": {
       "version": "1.3.0",
       "resolved": "https://registry.npmjs.org/component-emitter/-/component-emitter-1.3.0.tgz",
@@ -9963,6 +9976,11 @@
       "resolved": "https://registry.npmjs.org/escape-html/-/escape-html-1.0.3.tgz",
       "integrity": "sha1-Aljq5NPQwJdN4cFpGI7wBR0dGYg="
     },
+    "node_modules/escape-latex": {
+      "version": "1.2.0",
+      "resolved": "https://registry.npmjs.org/escape-latex/-/escape-latex-1.2.0.tgz",
+      "integrity": "sha512-nV5aVWW1K0wEiUIEdZ4erkGGH8mDxGyxSeqPzRNtWP7ataw+/olFObw7hujFWlVjNsaDFw5VZ5NzVSIqRgfTiw=="
+    },
     "node_modules/escape-string-regexp": {
       "version": "4.0.0",
       "resolved": "https://registry.npmjs.org/escape-string-regexp/-/escape-string-regexp-4.0.0.tgz",
@@ -14273,6 +14291,11 @@
       "integrity": "sha1-R+Y/evVa+m+S4VAOaQ64uFKcCZo=",
       "dev": true
     },
+    "node_modules/javascript-natural-sort": {
+      "version": "0.7.1",
+      "resolved": "https://registry.npmjs.org/javascript-natural-sort/-/javascript-natural-sort-0.7.1.tgz",
+      "integrity": "sha512-nO6jcEfZWQXDhOiBtG2KvKyEptz7RVbpGP4vTD2hLBdmNQSsCiicO2Ioinv6UI4y9ukqnBpy+XZ9H6uLNgJTlw=="
+    },
     "node_modules/javascript-stringify": {
       "version": "2.1.0",
       "resolved": "https://registry.npmjs.org/javascript-stringify/-/javascript-stringify-2.1.0.tgz",
@@ -15516,6 +15539,28 @@
         "speech-rule-engine": "^4.0.6"
       }
     },
+    "node_modules/mathjs": {
+      "version": "10.6.1",
+      "resolved": "https://registry.npmjs.org/mathjs/-/mathjs-10.6.1.tgz",
+      "integrity": "sha512-8iZp6uUKKBoCFoUHze9ydsrSji9/IOEzMhwURyoQXaLL1+ILEZnraw4KzZnUBt/XN6lPJPV+7JO94oil3AmosQ==",
+      "dependencies": {
+        "@babel/runtime": "^7.18.3",
+        "complex.js": "^2.1.1",
+        "decimal.js": "^10.3.1",
+        "escape-latex": "^1.2.0",
+        "fraction.js": "^4.2.0",
+        "javascript-natural-sort": "^0.7.1",
+        "seedrandom": "^3.0.5",
+        "tiny-emitter": "^2.1.0",
+        "typed-function": "^2.1.0"
+      },
+      "bin": {
+        "mathjs": "bin/cli.js"
+      },
+      "engines": {
+        "node": ">= 14"
+      }
+    },
     "node_modules/md5-file": {
       "version": "5.0.0",
       "resolved": "https://registry.npmjs.org/md5-file/-/md5-file-5.0.0.tgz",
@@ -22314,6 +22359,11 @@
       "resolved": "https://registry.npmjs.org/secure-json-parse/-/secure-json-parse-2.4.0.tgz",
       "integrity": "sha512-Q5Z/97nbON5t/L/sH6mY2EacfjVGwrCcSi5D3btRO2GZ8pf1K1UN7Z9H5J57hjVU2Qzxr1xO+FmBhOvEkzCMmg=="
     },
+    "node_modules/seedrandom": {
+      "version": "3.0.5",
+      "resolved": "https://registry.npmjs.org/seedrandom/-/seedrandom-3.0.5.tgz",
+      "integrity": "sha512-8OwmbklUNzwezjGInmZ+2clQmExQPvomqjL7LFqOYqtmuxRgQYqOD3mHaU+MvZn5FLUeVxVfQjwLZW/n/JFuqg=="
+    },
     "node_modules/select-hose": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/select-hose/-/select-hose-2.0.0.tgz",
@@ -24400,6 +24450,11 @@
       "integrity": "sha1-QFQRqOfmM5/mTbmiNN4R3DHgK9Q=",
       "dev": true
     },
+    "node_modules/tiny-emitter": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/tiny-emitter/-/tiny-emitter-2.1.0.tgz",
+      "integrity": "sha512-NB6Dk1A9xgQPMoGqC5CVXn123gWyte215ONT5Pp5a0yt4nlEoO1ZWeCwpncaekPHXO60i47ihFnZPiRPjRMq4Q=="
+    },
     "node_modules/tmp": {
       "version": "0.2.1",
       "resolved": "https://registry.npmjs.org/tmp/-/tmp-0.2.1.tgz",
@@ -25060,6 +25115,14 @@
         "node": ">= 0.6"
       }
     },
+    "node_modules/typed-function": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/typed-function/-/typed-function-2.1.0.tgz",
+      "integrity": "sha512-bctQIOqx2iVbWGDGPWwIm18QScpu2XRmkC19D8rQGFsjKSgteq/o1hTZvIG/wuDq8fanpBDrLkLq+aEN/6y5XQ==",
+      "engines": {
+        "node": ">= 10"
+      }
+    },
     "node_modules/typed-styles": {
       "version": "0.0.7",
       "resolved": "https://registry.npmjs.org/typed-styles/-/typed-styles-0.0.7.tgz",
@@ -28124,9 +28187,9 @@
       "integrity": "sha512-n2Q6i+fnJqzOaq2VkdXxy2TCPCWQZHiCo0XqmrCvDWcZQKRyZzYi4Z0yxlBuN0w+r2ZHmre+Q087DSrw3pbJDQ=="
     },
     "@babel/runtime": {
-      "version": "7.17.9",
-      "resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.17.9.tgz",
-      "integrity": "sha512-lSiBBvodq29uShpWGNbgFdKYNiFDo5/HIYsaCEY9ff4sb10x9jizo2+pRrSyF4jKZCXqgzuqBOQKbUm90gQwJg==",
+      "version": "7.18.3",
+      "resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.18.3.tgz",
+      "integrity": "sha512-38Y8f7YUhce/K7RMwTp7m0uCumpv9hZkitCbBClqQIow1qSbCvGkcegKOXpEWCQLfWmevgRiWokZ1GkpfhbZug==",
       "requires": {
         "regenerator-runtime": "^0.13.4"
       }
@@ -33810,6 +33873,11 @@
       "resolved": "https://registry.npmjs.org/commondir/-/commondir-1.0.1.tgz",
       "integrity": "sha1-3dgA2gxmEnOTzKWVDqloo6rxJTs="
     },
+    "complex.js": {
+      "version": "2.1.1",
+      "resolved": "https://registry.npmjs.org/complex.js/-/complex.js-2.1.1.tgz",
+      "integrity": "sha512-8njCHOTtFFLtegk6zQo0kkVX1rngygb/KQI6z1qZxlFI3scluC+LVTCFbrkWjBv4vvLlbQ9t88IPMC6k95VTTg=="
+    },
     "component-emitter": {
       "version": "1.3.0",
       "resolved": "https://registry.npmjs.org/component-emitter/-/component-emitter-1.3.0.tgz",
@@ -35968,6 +36036,11 @@
       "resolved": "https://registry.npmjs.org/escape-html/-/escape-html-1.0.3.tgz",
       "integrity": "sha1-Aljq5NPQwJdN4cFpGI7wBR0dGYg="
     },
+    "escape-latex": {
+      "version": "1.2.0",
+      "resolved": "https://registry.npmjs.org/escape-latex/-/escape-latex-1.2.0.tgz",
+      "integrity": "sha512-nV5aVWW1K0wEiUIEdZ4erkGGH8mDxGyxSeqPzRNtWP7ataw+/olFObw7hujFWlVjNsaDFw5VZ5NzVSIqRgfTiw=="
+    },
     "escape-string-regexp": {
       "version": "4.0.0",
       "resolved": "https://registry.npmjs.org/escape-string-regexp/-/escape-string-regexp-4.0.0.tgz",
@@ -39268,6 +39341,11 @@
       "integrity": "sha1-R+Y/evVa+m+S4VAOaQ64uFKcCZo=",
       "dev": true
     },
+    "javascript-natural-sort": {
+      "version": "0.7.1",
+      "resolved": "https://registry.npmjs.org/javascript-natural-sort/-/javascript-natural-sort-0.7.1.tgz",
+      "integrity": "sha512-nO6jcEfZWQXDhOiBtG2KvKyEptz7RVbpGP4vTD2hLBdmNQSsCiicO2Ioinv6UI4y9ukqnBpy+XZ9H6uLNgJTlw=="
+    },
     "javascript-stringify": {
       "version": "2.1.0",
       "resolved": "https://registry.npmjs.org/javascript-stringify/-/javascript-stringify-2.1.0.tgz",
@@ -40266,6 +40344,22 @@
         "speech-rule-engine": "^4.0.6"
       }
     },
+    "mathjs": {
+      "version": "10.6.1",
+      "resolved": "https://registry.npmjs.org/mathjs/-/mathjs-10.6.1.tgz",
+      "integrity": "sha512-8iZp6uUKKBoCFoUHze9ydsrSji9/IOEzMhwURyoQXaLL1+ILEZnraw4KzZnUBt/XN6lPJPV+7JO94oil3AmosQ==",
+      "requires": {
+        "@babel/runtime": "^7.18.3",
+        "complex.js": "^2.1.1",
+        "decimal.js": "^10.3.1",
+        "escape-latex": "^1.2.0",
+        "fraction.js": "^4.2.0",
+        "javascript-natural-sort": "^0.7.1",
+        "seedrandom": "^3.0.5",
+        "tiny-emitter": "^2.1.0",
+        "typed-function": "^2.1.0"
+      }
+    },
     "md5-file": {
       "version": "5.0.0",
       "resolved": "https://registry.npmjs.org/md5-file/-/md5-file-5.0.0.tgz",
@@ -45673,6 +45767,11 @@
       "resolved": "https://registry.npmjs.org/secure-json-parse/-/secure-json-parse-2.4.0.tgz",
       "integrity": "sha512-Q5Z/97nbON5t/L/sH6mY2EacfjVGwrCcSi5D3btRO2GZ8pf1K1UN7Z9H5J57hjVU2Qzxr1xO+FmBhOvEkzCMmg=="
     },
+    "seedrandom": {
+      "version": "3.0.5",
+      "resolved": "https://registry.npmjs.org/seedrandom/-/seedrandom-3.0.5.tgz",
+      "integrity": "sha512-8OwmbklUNzwezjGInmZ+2clQmExQPvomqjL7LFqOYqtmuxRgQYqOD3mHaU+MvZn5FLUeVxVfQjwLZW/n/JFuqg=="
+    },
     "select-hose": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/select-hose/-/select-hose-2.0.0.tgz",
@@ -47408,6 +47507,11 @@
       "integrity": "sha1-QFQRqOfmM5/mTbmiNN4R3DHgK9Q=",
       "dev": true
     },
+    "tiny-emitter": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/tiny-emitter/-/tiny-emitter-2.1.0.tgz",
+      "integrity": "sha512-NB6Dk1A9xgQPMoGqC5CVXn123gWyte215ONT5Pp5a0yt4nlEoO1ZWeCwpncaekPHXO60i47ihFnZPiRPjRMq4Q=="
+    },
     "tmp": {
       "version": "0.2.1",
       "resolved": "https://registry.npmjs.org/tmp/-/tmp-0.2.1.tgz",
@@ -47929,6 +48033,11 @@
         "mime-types": "~2.1.24"
       }
     },
+    "typed-function": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/typed-function/-/typed-function-2.1.0.tgz",
+      "integrity": "sha512-bctQIOqx2iVbWGDGPWwIm18QScpu2XRmkC19D8rQGFsjKSgteq/o1hTZvIG/wuDq8fanpBDrLkLq+aEN/6y5XQ=="
+    },
     "typed-styles": {
       "version": "0.0.7",
       "resolved": "https://registry.npmjs.org/typed-styles/-/typed-styles-0.0.7.tgz",
diff --git a/package.json b/package.json
index f7b16fd02..1a709681f 100644
--- a/package.json
+++ b/package.json
@@ -76,6 +76,7 @@
     "lodash": "^4.17.21",
     "markdown-it": "^12.2.0",
     "mathjax-full": "^3.2.1",
+    "mathjs": "^10.6.1",
     "mongodb": "4.3.1",
     "nanoid": "^3.3.4",
     "patch-package": "^6.4.7",

From 73495ff2315144ca9208964e6cc2a4cfefbc8bd8 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Thu, 2 Jun 2022 18:49:15 +0200
Subject: [PATCH 04/62] added reduce and some code improvements

---
 .../vue/components/MiniComposer/gateUtils.ts  | 119 +++++++++---------
 1 file changed, 62 insertions(+), 57 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/gateUtils.ts b/frontend/vue/components/MiniComposer/gateUtils.ts
index 2a5b0e689..29f444554 100644
--- a/frontend/vue/components/MiniComposer/gateUtils.ts
+++ b/frontend/vue/components/MiniComposer/gateUtils.ts
@@ -1,5 +1,5 @@
 // eslint-disable-next-line import/named
-import { multiply, subtract, add } from 'mathjs'
+import { multiply, subtract, add, gcd, flatten, map, round } from 'mathjs'
 
 export enum GateName {
   UNKNOWN = 'UNKNOWN',
@@ -16,8 +16,6 @@ export enum GateName {
   MEASURE_Z = 'Measure'
 }
 
-const mult = multiply
-const sub = subtract
 function neg (m: number[][]) {
   return multiply(m, -1)
 }
@@ -29,6 +27,20 @@ export interface StateMatrix {
   m: number
 }
 
+function reduce (state: StateMatrix) {
+  const { A, B, C, D, m } = state
+  const matricesValues = flatten([...A, ...B, ...C, ...D]) as unknown as number[]
+  const d = gcd(...matricesValues, Math.pow(2, m))
+
+  return {
+    A: map(A, value => round(value / d)),
+    B: map(B, value => round(value / d)),
+    C: map(C, value => round(value / d)),
+    D: map(D, value => round(value / d)),
+    m: round(m / d)
+  }
+}
+
 export function IdentityState (): StateMatrix {
   return {
     A: [[1, 0], [0, 1]],
@@ -45,7 +57,6 @@ export interface QuantumGate {
 
 export const Identity: QuantumGate = {
   apply (state: StateMatrix) {
-    // Integer part
     return state
   }
 }
@@ -54,13 +65,13 @@ export const XGate: QuantumGate = {
   apply (state: StateMatrix) {
     // Integer part
     const K = [[0, 1], [1, 0]]
-    return {
-      A: mult(K, state.A),
-      B: mult(K, state.B),
-      C: mult(K, state.C),
-      D: mult(K, state.D),
+    return reduce({
+      A: multiply(K, state.A),
+      B: multiply(K, state.B),
+      C: multiply(K, state.C),
+      D: multiply(K, state.D),
       m: state.m
-    }
+    })
   }
 }
 
@@ -69,13 +80,13 @@ export const YGate: QuantumGate = {
     // Integer part
     const K = [[0, -1], [1, 0]]
 
-    return {
-      A: neg(mult(K, state.B)),
-      B: mult(K, state.A),
-      C: neg(mult(K, state.D)),
-      D: mult(K, state.C),
+    return reduce({
+      A: neg(multiply(K, state.B)),
+      B: multiply(K, state.A),
+      C: neg(multiply(K, state.D)),
+      D: multiply(K, state.C),
       m: state.m
-    }
+    })
   }
 }
 
@@ -84,13 +95,13 @@ export const ZGate: QuantumGate = {
     // Integer part
     const K = [[1, 0], [0, -1]]
 
-    return {
-      A: mult(K, state.A),
-      B: mult(K, state.B),
-      C: mult(K, state.C),
-      D: mult(K, state.D),
+    return reduce({
+      A: multiply(K, state.A),
+      B: multiply(K, state.B),
+      C: multiply(K, state.C),
+      D: multiply(K, state.D),
       m: state.m
-    }
+    })
   }
 }
 
@@ -99,13 +110,13 @@ export const HGate: QuantumGate = {
     // Integer part
     const K = [[1, 1], [1, -1]]
 
-    return {
-      A: mult(mult(K, state.C), 2),
-      B: mult(mult(K, state.D), 2),
-      C: mult(K, state.A),
-      D: mult(K, state.B),
+    return reduce({
+      A: multiply(multiply(K, state.C), 2),
+      B: multiply(multiply(K, state.D), 2),
+      C: multiply(K, state.A),
+      D: multiply(K, state.B),
       m: state.m + 1
-    }
+    })
   }
 }
 
@@ -115,13 +126,13 @@ export const SGate: QuantumGate = {
     const K1 = [[1, 0], [0, 0]]
     const K2 = [[0, 0], [0, 1]]
 
-    return {
-      A: sub(mult(K1, state.A), mult(K2, state.B)),
-      B: add(mult(K2, state.A), mult(K1, state.B)),
-      C: sub(mult(K1, state.C), mult(K2, state.D)),
-      D: add(mult(K1, state.C), mult(K1, state.D)),
+    return reduce({
+      A: subtract(multiply(K1, state.A), multiply(K2, state.B)),
+      B: add(multiply(K2, state.A), multiply(K1, state.B)),
+      C: subtract(multiply(K1, state.C), multiply(K2, state.D)),
+      D: add(multiply(K1, state.C), multiply(K1, state.D)),
       m: state.m
-    }
+    })
   }
 }
 
@@ -131,24 +142,24 @@ export const TGate: QuantumGate = {
     const K1 = [[2, 0], [0, 0]]
     const K2 = [[0, 0], [0, 1]]
 
-    const K1_A = mult(K1, state.A)
-    const K1_B = mult(K1, state.B)
-    const K1_C = mult(K1, state.C)
-    const K1_D = mult(K1, state.D)
-    const K2_A = mult(K2, state.A)
-    const K2_B = mult(K2, state.B)
-    const K2_C = mult(K2, state.C)
-    const K2_D = mult(K2, state.D)
-    const K2_C_2 = mult(K2_C, 2)
-    const K2_D_2 = mult(K2_D, 2)
-
-    return {
-      A: sub(add(K1_A, K2_C_2), K2_D_2),
+    const K1_A = multiply(K1, state.A)
+    const K1_B = multiply(K1, state.B)
+    const K1_C = multiply(K1, state.C)
+    const K1_D = multiply(K1, state.D)
+    const K2_A = multiply(K2, state.A)
+    const K2_B = multiply(K2, state.B)
+    const K2_C = multiply(K2, state.C)
+    const K2_D = multiply(K2, state.D)
+    const K2_C_2 = multiply(K2_C, 2)
+    const K2_D_2 = multiply(K2_D, 2)
+
+    return reduce({
+      A: subtract(add(K1_A, K2_C_2), K2_D_2),
       B: add(add(K1_B, K2_C_2), K2_D_2),
-      C: add(sub(K2_A, K2_B), K1_C),
+      C: add(subtract(K2_A, K2_B), K1_C),
       D: add(add(K2_A, K2_B), K1_D),
       m: state.m + 1
-    }
+    })
   }
 }
 
@@ -179,19 +190,13 @@ function signedString (value: number, symbol: string) {
 function StateMatrixElementToTex (state: StateMatrix, coords: { x: number, y: number }) {
   const { x, y } = coords
   const [a, b, c, d] = [state.A[x][y], state.B[x][y], state.C[x][y], state.D[x][y]]
-  const isZero = (Math.pow(a, 2) + Math.pow(b, 2) + Math.pow(c, 2) + Math.pow(d, 2)) === 0
+  const isZero = (a * a + b * b + c * c + d * d) === 0
 
   if (isZero) {
     return '0'
   }
 
-  let tex = ''
-
-  if (a !== 0) {
-    tex = `${tex}${a}`
-  }
-
-  tex = `${tex}${signedString(b, 'i')}${signedString(c, '\\sqrt{2}')}${signedString(d, 'i\\sqrt{2}')}`
+  let tex = `${a || ''}${signedString(b, 'i')}${signedString(c, '\\sqrt{2}')}${signedString(d, 'i\\sqrt{2}')}`
 
   if (tex.startsWith('+')) {
     tex = tex.substring(1)

From 98839701601af306fca8636d3ad446d2cc0abc62 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Thu, 2 Jun 2022 19:27:32 +0200
Subject: [PATCH 05/62] media query added

---
 .../components/MiniComposer/CircuitSandboxWidget.vue   | 10 ++++++++++
 1 file changed, 10 insertions(+)

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index a936dde7e..4684a28b7 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -184,6 +184,16 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
     "gates lesson"
     "circuit lesson";
 
+  @include mq ($until: medium) {
+    grid-template-columns: 1fr;
+    grid-template-rows: min-content min-content min-content min-content;
+    grid-template-areas:
+      "text"
+      "gates"
+      "circuit"
+      "lesson";
+  }
+
   &__config-container {
     display: none;
   }

From 09865f74fc786cf47b7b91290d1fa60f279e93e5 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Fri, 3 Jun 2022 12:43:19 +0200
Subject: [PATCH 06/62] changed fractions to independent fractions

---
 .../vue/components/MiniComposer/gateUtils.ts  | 45 ++++++++++++++-----
 1 file changed, 33 insertions(+), 12 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/gateUtils.ts b/frontend/vue/components/MiniComposer/gateUtils.ts
index 29f444554..db26d43a7 100644
--- a/frontend/vue/components/MiniComposer/gateUtils.ts
+++ b/frontend/vue/components/MiniComposer/gateUtils.ts
@@ -41,6 +41,15 @@ function reduce (state: StateMatrix) {
   }
 }
 
+function reduceSingleElement (numerator: number, denominator: number) {
+  const d = gcd(numerator, denominator)
+
+  return {
+    numerator: round(numerator / d),
+    denominator: round(denominator / d)
+  }
+}
+
 export function IdentityState (): StateMatrix {
   return {
     A: [[1, 0], [0, 1]],
@@ -178,13 +187,27 @@ export const gateMap = {
   [GateName.RZ]: Identity
 }
 
-function signedString (value: number, symbol: string) {
-  if (value === 0) {
+function signedString (n: number, m: number, symbol: string = '') {
+  if (n === 0) {
     return ''
   }
+  const { numerator, denominator } = reduceSingleElement(n, Math.pow(2, m))
+
+  const absNumerator = Math.abs(numerator)
+  const sign = numerator > 0 ? '+' : '-'
+  let numeratorTex = ''
+
+  if (symbol) {
+    numeratorTex = `${absNumerator > 1 ? absNumerator : ''}${symbol}`
+  } else {
+    numeratorTex = `${absNumerator}`
+  }
 
-  const absValue = Math.abs(value)
-  return `${value > 0 ? '+' : '-'}${absValue > 1 ? absValue : ''}${symbol}`
+  if (m > 0) {
+    return `${sign}\\frac{${numeratorTex}}{${denominator}}`
+  } else {
+    return `${sign}${numeratorTex}`
+  }
 }
 
 function StateMatrixElementToTex (state: StateMatrix, coords: { x: number, y: number }) {
@@ -196,16 +219,12 @@ function StateMatrixElementToTex (state: StateMatrix, coords: { x: number, y: nu
     return '0'
   }
 
-  let tex = `${a || ''}${signedString(b, 'i')}${signedString(c, '\\sqrt{2}')}${signedString(d, 'i\\sqrt{2}')}`
+  let tex = `${signedString(a, state.m)}${signedString(b, state.m, 'i')}${signedString(c, state.m, '\\sqrt{2}')}${signedString(d, state.m, 'i\\sqrt{2}')}`
 
   if (tex.startsWith('+')) {
     tex = tex.substring(1)
   }
 
-  if (state.m > 0) {
-    tex = `\\frac{${tex}}{${Math.pow(2, state.m)}}`
-  }
-
   return tex
 }
 
@@ -227,16 +246,18 @@ export function StateMatrixToTexKetNotation (state: StateMatrix) {
 
   let zeroKetTex = ''
   let oneKetTex = ''
+  const bothKets = zeroKetValue !== '0' && oneKetValue !== '0'
+
   if (zeroKetValue !== '0') {
-    zeroKetTex = `${zeroKetValue === '1' ? '' : zeroKetValue}${ZERO_KET}`
+    zeroKetTex = `${bothKets ? '(' : ''}${zeroKetValue === '1' ? '' : zeroKetValue}${ZERO_KET}${bothKets ? ')' : ''}`
   }
 
   if (oneKetValue !== '0') {
-    oneKetTex = `${oneKetValue === '1' ? '' : oneKetValue}${ONE_KET}`
+    oneKetTex = `${bothKets ? '(' : ''}${oneKetValue === '1' ? '' : oneKetValue}${ONE_KET}${bothKets ? ')' : ''}`
   }
 
   let joinTex = ''
-  if (zeroKetTex && oneKetTex && !oneKetTex.startsWith('-')) {
+  if (bothKets && !oneKetTex.startsWith('-')) {
     joinTex = '+'
   }
 

From e15850c0308000b728ff29561070658987c4431e Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Fri, 3 Jun 2022 14:28:20 +0200
Subject: [PATCH 07/62] added S gate

---
 frontend/vue/components/MiniComposer/Gate.vue | 3 +++
 notebooks/examples/widgets.ipynb              | 2 +-
 2 files changed, 4 insertions(+), 1 deletion(-)

diff --git a/frontend/vue/components/MiniComposer/Gate.vue b/frontend/vue/components/MiniComposer/Gate.vue
index c814a716a..bc5c2144a 100644
--- a/frontend/vue/components/MiniComposer/Gate.vue
+++ b/frontend/vue/components/MiniComposer/Gate.vue
@@ -15,6 +15,9 @@
     <div v-if="name === gateName.T" class="gate__symbol gate__symbol_text">
       T
     </div>
+    <div v-if="name === gateName.S" class="gate__symbol gate__symbol_text">
+      S
+    </div>
     <div v-if="isRotationGate()" class="gate__symbol gate__symbol_text">
       {{ name }}
       <div v-if="rotation" class="gate__symbol__rotation">
diff --git a/notebooks/examples/widgets.ipynb b/notebooks/examples/widgets.ipynb
index 8c7a66bfe..c71b10912 100644
--- a/notebooks/examples/widgets.ipynb
+++ b/notebooks/examples/widgets.ipynb
@@ -16,7 +16,7 @@
     "    q-circuit-sandbox-widget(goal=\"minicomposer\")\n",
     "        .slide\n",
     "            .circuit\n",
-    "                .availableGates H X Z Y T\n",
+    "                .availableGates H X Z Y T S\n",
     "                .initialCircuit\n",
     "                    .qubit\n",
     "            .instructions first slide instructions\n",

From 798c126a44a7526e9ade58908dc3922de63e9c74 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Fri, 3 Jun 2022 14:42:49 +0200
Subject: [PATCH 08/62] changed goal in widgets.ipynb

---
 notebooks/examples/widgets.ipynb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/notebooks/examples/widgets.ipynb b/notebooks/examples/widgets.ipynb
index c71b10912..885738e99 100644
--- a/notebooks/examples/widgets.ipynb
+++ b/notebooks/examples/widgets.ipynb
@@ -11,9 +11,9 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "## minicomposer\n",
+    "## Circuit sandbox\n",
     "\n",
-    "    q-circuit-sandbox-widget(goal=\"minicomposer\")\n",
+    "    q-circuit-sandbox-widget(goal=\"circuit-sandbox\")\n",
     "        .slide\n",
     "            .circuit\n",
     "                .availableGates H X Z Y T S\n",

From af799ce6293bc09128fd93d2c234532d7a92f90d Mon Sep 17 00:00:00 2001
From: techtolentino <makertolentino@gmail.com>
Date: Fri, 3 Jun 2022 11:30:42 -0700
Subject: [PATCH 09/62] update cta w/ segment info

---
 .../UserAccount/ClassroomSection.vue          | 19 ++++++++++++++-----
 1 file changed, 14 insertions(+), 5 deletions(-)

diff --git a/frontend/vue/components/UserAccount/ClassroomSection.vue b/frontend/vue/components/UserAccount/ClassroomSection.vue
index 58eff31dd..cde034291 100644
--- a/frontend/vue/components/UserAccount/ClassroomSection.vue
+++ b/frontend/vue/components/UserAccount/ClassroomSection.vue
@@ -11,8 +11,9 @@
     <div class="classroom__create-syllabus">
       <AppCta
         class="classroom__create-syllabus__button"
-        :label="$translate('Create a Syllabus')"
-        url="/syllabus/create"
+        :label="createSyllabusCTA.label"
+        :url="createSyllabusCTA.url"
+        :segment="createSyllabusCTA.segment"
       />
       <p class="classroom__create-syllabus__description">
         {{ $translate("Create a curated learning path for your students, using Qiskit Textbook Chapters, Labs, and Summer Schools") }}
@@ -40,9 +41,9 @@
 <script lang="ts">
 import { defineComponent } from 'vue-demi'
 import AppCta from '../common/AppCta.vue'
+import { getSyllabi, Syllabus } from '../../../ts/syllabus'
 import UserAccountSectionHeader from './UserAccountSectionHeader.vue'
 import SyllabusCard from './SyllabusCard.vue'
-import { getSyllabi, Syllabus } from '../../../ts/syllabus'
 
 export default defineComponent({
   name: 'ClassRoomSection',
@@ -54,10 +55,18 @@ export default defineComponent({
   data () {
     return {
       // TODO: REPLACE MOCK DATA
-      syllabi: ([] as  Syllabus[])
+      syllabi: ([] as Syllabus[]),
+      createSyllabusCTA: {
+        label: this.$translate('Create a Syllabus'),
+        url: '/syllabus/create',
+        segment: {
+          cta: 'syllabus-create',
+          location: 'user-account-classroom'
+        }
+      }
     }
   },
-  mounted() {
+  mounted () {
     getSyllabi().then((syllabi: Syllabus[]) => {
       this.syllabi = syllabi
     })

From 1dcf2b56b03e7ac396a3c6638097754dea6106a5 Mon Sep 17 00:00:00 2001
From: kifumi <kifumi@jp.ibm.com>
Date: Mon, 6 Jun 2022 16:59:46 +0900
Subject: [PATCH 10/62] Update HowtoTranslate_QiskitTextbook_ja.pdf

Updated the last page for proofreading.
---
 .../HowtoTranslate_QiskitTextbook_ja.pdf      | Bin 3295470 -> 3320517 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/translations/HowtoTranslate_QiskitTextbook_ja.pdf b/translations/HowtoTranslate_QiskitTextbook_ja.pdf
index 8b0d35b5eb3f86c6de8abf585456d20ce774fc40..634c65acdb1bd4e97b4fbbd3f97a8023d0498e2d 100644
GIT binary patch
delta 182456
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From 00016126d2d829e4c56c1ba63e96d411918dc9f5 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Tue, 7 Jun 2022 17:19:17 +0200
Subject: [PATCH 11/62] visualization changes

---
 frontend/vue/components/MiniComposer/MatrixView.vue | 0
 frontend/vue/components/MiniComposer/gateUtils.ts   | 8 ++++----
 2 files changed, 4 insertions(+), 4 deletions(-)
 delete mode 100644 frontend/vue/components/MiniComposer/MatrixView.vue

diff --git a/frontend/vue/components/MiniComposer/MatrixView.vue b/frontend/vue/components/MiniComposer/MatrixView.vue
deleted file mode 100644
index e69de29bb..000000000
diff --git a/frontend/vue/components/MiniComposer/gateUtils.ts b/frontend/vue/components/MiniComposer/gateUtils.ts
index db26d43a7..965b8265f 100644
--- a/frontend/vue/components/MiniComposer/gateUtils.ts
+++ b/frontend/vue/components/MiniComposer/gateUtils.ts
@@ -230,10 +230,10 @@ function StateMatrixElementToTex (state: StateMatrix, coords: { x: number, y: nu
 
 export function StateMatrixToTexMatrix (state: StateMatrix) {
   return `
-    \\begin{bmatrix}
+    \\begin{pmatrix}
       ${StateMatrixElementToTex(state, { x: 0, y: 0 })} & ${StateMatrixElementToTex(state, { x: 0, y: 1 })}\\\\
       ${StateMatrixElementToTex(state, { x: 1, y: 0 })} & ${StateMatrixElementToTex(state, { x: 1, y: 1 })}
-    \\end{bmatrix}
+    \\end{pmatrix}
   `
 }
 
@@ -249,11 +249,11 @@ export function StateMatrixToTexKetNotation (state: StateMatrix) {
   const bothKets = zeroKetValue !== '0' && oneKetValue !== '0'
 
   if (zeroKetValue !== '0') {
-    zeroKetTex = `${bothKets ? '(' : ''}${zeroKetValue === '1' ? '' : zeroKetValue}${ZERO_KET}${bothKets ? ')' : ''}`
+    zeroKetTex = `${bothKets ? '\\left(' : ''}${zeroKetValue === '1' ? '' : zeroKetValue}${bothKets ? '\\right)' : ''}${ZERO_KET}`
   }
 
   if (oneKetValue !== '0') {
-    oneKetTex = `${bothKets ? '(' : ''}${oneKetValue === '1' ? '' : oneKetValue}${ONE_KET}${bothKets ? ')' : ''}`
+    oneKetTex = `${bothKets ? '\\left(' : ''}${oneKetValue === '1' ? '' : oneKetValue}${bothKets ? '\\right)' : ''}${ONE_KET}`
   }
 
   let joinTex = ''

From 409afd590f4cbf055bf9938452e360aae21c26b0 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Tue, 7 Jun 2022 17:31:53 +0200
Subject: [PATCH 12/62] infinite pool for gates

---
 .../vue/components/MiniComposer/CircuitSandboxWidget.vue | 9 ++++++---
 1 file changed, 6 insertions(+), 3 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index 4684a28b7..7d1a73ade 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -93,7 +93,10 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
 
   autoMeasureGate: boolean = false
 
-  availableGates: ComposerGate[] = []
+  initialAvailableGates: ComposerGate[] = []
+  get availableGates (): ComposerGate[] {
+    return this.initialAvailableGates.map(gate => gate)
+  }
 
   circuitState: ComposerGate[][] = [[]]
 
@@ -132,9 +135,9 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
     this.autoMeasureGate = !!htmlConfigElement.querySelector('.autoMeasureGate')
 
     const availableGatesElement = htmlConfigElement.querySelector('.availableGates') as HTMLElement
-    this.availableGates = []
+    this.initialAvailableGates = []
     if (availableGatesElement && availableGatesElement.textContent) {
-      this.availableGates = this.stringToGateNameArray(availableGatesElement.textContent)
+      this.initialAvailableGates = this.stringToGateNameArray(availableGatesElement.textContent)
     }
 
     const initialCircuitElement = Array.from<HTMLElement>(htmlConfigElement.querySelectorAll('.initialCircuit .qubit'))

From ebdf225608848a82de4fbf6fdfad93f8b958fe64 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Wed, 8 Jun 2022 13:22:13 +0200
Subject: [PATCH 13/62] Fixed S Gate

---
 frontend/vue/components/MiniComposer/gateUtils.ts | 4 +++-
 1 file changed, 3 insertions(+), 1 deletion(-)

diff --git a/frontend/vue/components/MiniComposer/gateUtils.ts b/frontend/vue/components/MiniComposer/gateUtils.ts
index 965b8265f..a5f621be3 100644
--- a/frontend/vue/components/MiniComposer/gateUtils.ts
+++ b/frontend/vue/components/MiniComposer/gateUtils.ts
@@ -139,7 +139,7 @@ export const SGate: QuantumGate = {
       A: subtract(multiply(K1, state.A), multiply(K2, state.B)),
       B: add(multiply(K2, state.A), multiply(K1, state.B)),
       C: subtract(multiply(K1, state.C), multiply(K2, state.D)),
-      D: add(multiply(K1, state.C), multiply(K1, state.D)),
+      D: add(multiply(K2, state.C), multiply(K1, state.D)),
       m: state.m
     })
   }
@@ -155,10 +155,12 @@ export const TGate: QuantumGate = {
     const K1_B = multiply(K1, state.B)
     const K1_C = multiply(K1, state.C)
     const K1_D = multiply(K1, state.D)
+
     const K2_A = multiply(K2, state.A)
     const K2_B = multiply(K2, state.B)
     const K2_C = multiply(K2, state.C)
     const K2_D = multiply(K2, state.D)
+
     const K2_C_2 = multiply(K2_C, 2)
     const K2_D_2 = multiply(K2_D, 2)
 

From 5b665820cdd5fa483968fb5a369fcb796aed2888 Mon Sep 17 00:00:00 2001
From: derwind <uncertainty_principle_ss@yahoo.co.jp>
Date: Wed, 8 Jun 2022 14:13:12 +0000
Subject: [PATCH 14/62] Translate describing-quantum-computers.ipynb via
 GitLocalize

---
 .../intro/describing-quantum-computers.ipynb  | 674 ++++++++++++++++++
 1 file changed, 674 insertions(+)
 create mode 100644 translations/ja/intro/describing-quantum-computers.ipynb

diff --git a/translations/ja/intro/describing-quantum-computers.ipynb b/translations/ja/intro/describing-quantum-computers.ipynb
new file mode 100644
index 000000000..6d579f0e5
--- /dev/null
+++ b/translations/ja/intro/describing-quantum-computers.ipynb
@@ -0,0 +1,674 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "gloss": {
+          "complex-number": {
+            "text": "Complex numbers can be made from combinations of real and <a href='https://en.wikipedia.org/wiki/Imaginary_number'>imaginary numbers</a>. If you're not sure what this means, don't worry! You won't need to in this course (but you can <a href='https://en.wikipedia.org/wiki/Complex_number'>read more</a> if you're interested.",
+            "title": "Complex number"
+          },
+          "esoteric": {
+            "text": "Esoteric words are specialized words that most people won't understand. We'll try to avoid them as much as possible, but they can be useful sometimes.",
+            "title": "esoteric"
+          },
+          "real-number": {
+            "text": "A real number is a number that only has a magnitude. If you've not heard of a real number before, you can probably drop the 'real' and just call them 'numbers'. Examples of real numbers include: 112, -5.4, and π. <a href='https://en.wikipedia.org/wiki/Real_number'>Read more</a>.",
+            "title": "Real number"
+          }
+        }
+      },
+      "source": [
+        "# 量子コンピューターの記述\n",
+        "\n",
+        "この章では、量子コンピューターを記述するために使用する様々な数学的オブジェクトと表記法を紹介します。記号や方程式、専門的な語彙を使うことで、非常に簡潔に数学と向き合い、コミュニケーションすることができます。しかし、記号の意味を知らないと理解するのが難しく、人を遠ざけることにもなりかねません。そこで、このテキストブックでは、数式をインタラクティブに表示します。記号の上にマウスを乗せると、その記号が何を意味しているかがわかります。また、数学や量子コンピューターの言葉を話せるようになるために、[難解な](gloss:esoteric)単語を少しずつ散りばめ、これらの単語にマウスを乗せると、その単語の解説を見ることができるようになっています。\n",
+        "\n",
+        "## 振幅\n",
+        "\n",
+        "古典的な確率は0から1の間の[実数](gloss:real-number)で表されることが多いですが、振幅は方向も持っています。振幅を表現するための自然な候補は[複素数](gloss:complex-number)です。複素数も大きさと方向の両方で完全に記述できますが、このコースでは、2方向（例えば左と右）を指す振幅だけを扱い、それ以外は気にしないことにしています。\n",
+        "\n",
+        "![振幅と確率を比較する画像](images/quantum-states/prob-vs-amp.svg)\n",
+        "\n",
+        "これにより、計算が非常にシンプルになります。つまり、振幅を-1から+1までの数字で表すことができ、その数字が正であれば振幅は前を向き、負であれば後ろを向いていることになるからです。しかし、これでも十分に面白いことができることがわかります。\n",
+        "\n",
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### クイッククイズ\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"intro-describing-0\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\n",
+        "このうち、有効な振幅ではあるが、有効な確率では*ない*ものはどれか？\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option(correct) -->\n",
+        "\n",
+        "1. $-1$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $1/3$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $1.01$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $\\sqrt{-2}$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "formulas": {
+          "_amp-0-0": {
+            "meaning": "This is the amplitude of the two-qubit state <code>00</code>, it's equal to the square-root of a half."
+          },
+          "_amp-1-0": {
+            "meaning": "This is the amplitude of the two-qubit state <code>01</code>, it's equal to the square-root of a half."
+          },
+          "_amp-2-0": {
+            "meaning": "This is the amplitude of the two-qubit state <code>10</code>, it's equal to 0."
+          },
+          "_amp-3-0": {
+            "meaning": "This is the amplitude of the two-qubit state <code>11</code>, it's equal to 0."
+          },
+          "def-equal": {
+            "meaning": "This means we are defining the things on the left of this symbol to be equal to the things on the right of this symbol."
+          },
+          "x-ket": {
+            "meaning": "This is a vector we have labelled '|x⟩', the '|' and '⟩' remind us this label refers to a vector.",
+            "say": "ket x"
+          }
+        }
+      },
+      "source": [
+        "## 状態ベクトル\n",
+        "\n",
+        "We saw in the last page that we can predict the behaviour of a quantum system by keeping track of the probability amplitudes for each outcome at each point in our computation. We also saw that, for n qubits, there are $2^n$ possible outcomes, and we can store these amplitudes in lists of length $2^n$ which we call vectors. Since these vectors describe the state of our qubits, we call them “state vectors”.\n",
+        "\n",
+        "ここでは、2つの量子ビットを持つ量子コンピューターの状態ベクトルの例を示します。\n",
+        "\n",
+        "$$\\class{x-ket}{|x\\rangle} \\class{def-equal}{:=} \\begin{bmatrix}\\cssId{_amp-0-0}{\\sqrt{\\tfrac{1}{2}}} \\ \\cssId{_amp-1-0}{\\sqrt{\\tfrac{1}{2}}} \\ \\cssId{_amp-2-0}{0} \\ \\cssId{_amp-3-0}{0} \\end{bmatrix}$$\n",
+        "\n",
+        "上の式のツールチップを読んでから、以下の質問に答えてください。\n",
+        "\n",
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### クイッククイズ\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"intro-describing-1\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\n",
+        "上の状態ベクトルにおいて、結果'01'の*振幅*は何か？\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $1$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option(correct) -->\n",
+        "\n",
+        "1. $\\sqrt{\\tfrac{1}{2}}$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $1/2$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $0$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "---\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"intro-describing-2\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\n",
+        "If the state vector above described the state of some qubits, what would be the *probability* of measuring ‘00’?\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $1$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $\\sqrt{\\tfrac{1}{2}}$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option(correct) -->\n",
+        "\n",
+        "1. $1/2$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $0$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "formulas": {
+          "_amp-0-1": {
+            "meaning": "Multiplying this number by the scalar on the left of the vector gives us the amplitude of the state <code>00</code>."
+          },
+          "_amp-0-general": {
+            "meaning": "This is the amplitude of the state <code>00</code>."
+          },
+          "_amp-1-1": {
+            "meaning": "Multiplying this number by the scalar on the left of the vector gives us the amplitude of the state <code>01</code>."
+          },
+          "_amp-1-general": {
+            "meaning": "This is the amplitude of the state <code>01</code>."
+          },
+          "_amp-2-1": {
+            "meaning": "Multiplying this number by the scalar on the left of the vector gives us the amplitude of the state <code>10</code>."
+          },
+          "_amp-2-general": {
+            "meaning": "This is the amplitude of the state <code>10</code>."
+          },
+          "_amp-3-1": {
+            "meaning": "Multiplying this number by the scalar on the left of the vector gives us the amplitude of the state <code>11</code>."
+          },
+          "_amp-3-general": {
+            "meaning": "This is the amplitude of the state <code>11</code>."
+          },
+          "_number-three": {
+            "meaning": "This is just the normal number <a href='https://en.wikipedia.org/wiki/3'>three</a>. Because it's immediately next to the vector, it means we are multiplying the vector by this number.",
+            "say": "Three"
+          },
+          "_psi-ket": {
+            "meaning": "This is a vector we have labelled '|ψ⟩', the '|' and '⟩' remind us this label refers to a vector. The character 'ψ' is written 'psi' in english.",
+            "say": "ket sigh (the 'p' is silent)"
+          },
+          "_sq-amp0": {
+            "meaning": "This number is proportional to the amplitude of the state <code>0</code>."
+          },
+          "_sq-amp1": {
+            "meaning": "This number is proportional to the amplitude of the state <code>1</code>."
+          },
+          "_vec-el-0": {
+            "meaning": "This is the zeroth element of the vector."
+          },
+          "_vec-el-1": {
+            "meaning": "This is the first element of the vector."
+          },
+          "_vec-el-2": {
+            "meaning": "This is the second element of the vector."
+          },
+          "_vec-el-3": {
+            "meaning": "This is the third element of the vector."
+          },
+          "_vec-el-n": {
+            "meaning": "This is the (N-1)th element of the vector. Since there are N elements (and we started counting at 0), this is also the last element."
+          },
+          "def-00": {
+            "meaning": "This is a statevector we are defining here (but is also a common convention in quantum computing) which corresponds to being in the state <code>00</code> with certainty."
+          },
+          "def-01": {
+            "meaning": "This is a statevector we are defining here (but is also a common convention in quantum computing) which corresponds to being in the state <code>01</code> with certainty."
+          },
+          "def-10": {
+            "meaning": "This is a statevector we are defining here (but is also a common convention in quantum computing) which corresponds to being in the state <code>10</code> with certainty."
+          },
+          "def-11": {
+            "meaning": "This is a statevector we are defining here (but is also a common convention in quantum computing) which corresponds to being in the state <code>11</code> with certainty."
+          },
+          "dots": {
+            "meaning": "These dots mean \"and so on\", implying a continuing pattern."
+          },
+          "equals": {
+            "meaning": "Everything to the left of this sign is equal to everything to the right of the sign.",
+            "say": "Equals"
+          },
+          "minus-ket": {
+            "meaning": "This is a vector we have labelled '|-⟩', the '|' and '⟩' remind us this label refers to a vector.",
+            "say": "ket minus"
+          },
+          "plus-ket": {
+            "meaning": "This is a vector we have labelled '|+⟩', the '|' and '⟩' remind us this label refers to a vector.",
+            "say": "ket plus"
+          },
+          "scalar": {
+            "meaning": "This is just a normal number. Because it's immediately next to the vector, it means we are multiplying (i.e. scaling) the vector by this number."
+          }
+        },
+        "gloss": {
+          "scalar-gloss": {
+            "text": "This is just a normal number, i.e. not a vector or matrix.",
+            "title": "Scalar"
+          }
+        }
+      },
+      "source": [
+        "## ベクトルの足し算と掛け算\n",
+        "\n",
+        "数学の他の分野を勉強すると、多くのものがベクトルとみなされることがわかります。ベクトルを「数のリスト」として紹介したのは、このテキストブックでもQiskitでもこのように考えるからです。しかし、ベクトルをただの数字のリストと区別するのは、数学者が2つのベクトルの足し算や、ベクトルと[スカラー](gloss:scalar-gloss)の掛け算について、明確に定義した規則を決めたからです。\n",
+        "\n",
+        "### ベクトルにスカラーを掛ける\n",
+        "\n",
+        "例えば、ここにスカラーを掛けたベクトルがあります。\n",
+        "\n",
+        "$$ \\cssId{_number-three}{3} \\begin{bmatrix} \\class{_vec-el-0}{1} \\ \\class{_vec-el-1}{2} \\ \\class{_vec-el-2}{-1} \\ \\class{_vec-el-3}{\\tfrac{1}{2}} \\ \\end{bmatrix} \\class{equals}{=} \\begin{bmatrix} \\class{_vec-el-0}{3} \\ \\class{_vec-el-1}{6} \\ \\class{_vec-el-2}{-3} \\ \\class{_vec-el-3}{\\tfrac{3}{2}} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "ベクトルの各要素が3倍されていることがわかります。要素を $N$ 個持つベクトルのより一般的な規則は次の通りです。\n",
+        "\n",
+        "$$ \\class{scalar}{s} \\begin{bmatrix} \\class{_vec-el-0}{e_0} \\ \\class{_vec-el-1}{e_1} \\ \\class{_vec-el-2}{e_2} \\ \\class{dots}{\\vdots} \\ \\class{*vec-el-n}{e*{N-1}} \\ \\end{bmatrix} \\class{equals}{=} \\begin{bmatrix} \\class{_vec-el-0}{s\\times e_0} \\ \\class{_vec-el-1}{s\\times e_1} \\ \\class{_vec-el-2}{s\\times e_2} \\ \\class{dots}{\\vdots} \\ \\class{*vec-el-n}{s\\times e*{N-1}} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "そこで、上で定義した状態ベクトル $|x\\rangle$ をもっときれいに書くと、次のようになります。\n",
+        "\n",
+        "$$ \\class{x-ket}{|x\\rangle} = \\class{scalar}{\\sqrt{\\tfrac{1}{2}}} \\begin{bmatrix} \\cssId{_amp-0-1}{1} \\ \\cssId{_amp-1-1}{1} \\ \\cssId{_amp-2-1}{0} \\ \\cssId{_amp-3-1}{0} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "### 2つのベクトルを足し合わせる\n",
+        "\n",
+        "The second rule is for adding two vectors together. This is only defined when the two vectors have the same number of elements, and gives a new vector with the same number of elements. Here is the general rule:\n",
+        "\n",
+        "$$ \\begin{bmatrix} \\class{_vec-el-0}{a_0} \\ \\class{_vec-el-1}{a_1} \\ \\class{_vec-el-2}{a_2} \\ \\class{_vec-el-3}{a_3} \\ \\class{dots}{\\vdots} \\ \\class{*vec-el-n}{a*{N-1}} \\ \\end{bmatrix} + \\begin{bmatrix} \\class{_vec-el-0}{b_0} \\ \\class{_vec-el-1}{b_1} \\ \\class{_vec-el-2}{b_2} \\ \\class{_vec-el-3}{b_3} \\ \\class{dots}{\\vdots} \\ \\class{*vec-el-n}{b*{N-1}} \\ \\end{bmatrix} \\class{equals}{=} \\begin{bmatrix} \\class{_vec-el-0}{a_0 + b_0} \\ \\class{_vec-el-1}{a_1 + b_1} \\ \\class{_vec-el-2}{a_2 + b_2} \\ \\class{<em data-md-type=\"emphasis\">vec-el-3}{a_3 + b_3} \\ \\class{dots}{\\vdots} \\ \\class{*vec-el-n}{a*{N-1} + b</em>{N-1}} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "つまり、ベクトルを足したり引いたりすることで、新しいベクトルを作ることができるのです。例えば、$|00\\rangle$ と $|01\\rangle$ というベクトルをそのように定義すると、以下のようになります。\n",
+        "\n",
+        "$$ \\class{def-00}{|00\\rangle} \\class{def-equal}{:=} \\begin{bmatrix} \\class{_amp-0-general}{1} \\ \\class{_amp-1-general}{0} \\ \\class{_amp-2-general}{0} \\ \\class{_amp-3-general}{0} \\end{bmatrix}, \\quad \\class{def-01}{|01\\rangle} \\class{def-equal}{:=} \\begin{bmatrix} \\class{_amp-0-general}{0} \\ \\class{_amp-1-general}{1} \\ \\class{_amp-2-general}{0} \\ \\class{_amp-3-general}{0} \\end{bmatrix} $$\n",
+        "\n",
+        "$\\class{x-ket}{|x\\rangle}$ を以下の形で書くことができます。\n",
+        "\n",
+        "$$\\class{x-ket}{|x\\rangle} = \\sqrt{\\tfrac{1}{2}}(\\class{def-00}{|00\\rangle} + \\class{def-01}{|01\\rangle})$$\n",
+        "\n",
+        "このように量子状態を足し合わせることを「重ね合わせ」と呼び、「$|x\\rangle$ は状態 $|00\\rangle$ と $|01\\rangle$ の重ね合わせである。」と表現することができます。実際、量子コンピューターでは、そのように計算基底状態を定義するのが慣例になっています。\n",
+        "\n",
+        "$$ \\class{def-00}{|00\\rangle} \\class{def-equal}{:=} \\begin{bmatrix} \\class{_amp-0-general}{1} \\ \\class{_amp-1-general}{0} \\ \\class{_amp-2-general}{0} \\ \\class{_amp-3-general}{0} \\end{bmatrix}, \\quad \\class{def-01}{|01\\rangle} \\class{def-equal}{:=} \\begin{bmatrix} \\class{_amp-0-general}{0} \\ \\class{_amp-1-general}{1} \\ \\class{_amp-2-general}{0} \\ \\class{_amp-3-general}{0} \\end{bmatrix}, \\quad \\class{def-10}{|10\\rangle} \\class{def-equal}{:=} \\begin{bmatrix} \\class{_amp-0-general}{0} \\ \\class{_amp-1-general}{0} \\ \\class{_amp-2-general}{1} \\ \\class{_amp-3-general}{0} \\end{bmatrix}, \\quad \\class{def-11}{|11\\rangle} \\class{def-equal}{:=} \\begin{bmatrix} \\class{_amp-0-general}{0} \\ \\class{_amp-1-general}{0} \\ \\class{_amp-2-general}{0} \\ \\class{_amp-3-general}{1} \\end{bmatrix} $$\n",
+        "\n",
+        "そして、それぞれのベクトルに正しい数を掛けて足し合わせれば、どんな量子状態もこれらの状態ベクトルの重ね合わせとして書くことができるのです。\n",
+        "\n",
+        "$$ \\cssId{_psi-ket}{|\\psi\\rangle} = \\class{*amp-0-general}{a*{00}}\\class{def-00}{|00\\rangle}\n",
+        "\n",
+        "- \\class{*amp-1-general}{a*{01}}\\class{def-01}{|01\\rangle}\n",
+        "- \\class{*amp-2-general}{a*{10}}\\class{def-10}{|10\\rangle}\n",
+        "- \\class{*amp-3-general}{a*{11}}\\class{def-11}{|11\\rangle} \\class{equals}{=} \\begin{bmatrix} \\class{*amp-0-general}{a*{00}} \\ \\class{*amp-1-general}{a*{01}} \\ \\class{*amp-2-general}{a*{10}} \\ \\class{*amp-3-general}{a*{11}} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "任意のベクトルをこの4つのベクトルの組み合わせとして書くことができるので、この4つのベクトルが基底を形成していると言い、これを「計算基底」と呼ぶことにします。計算基底は唯一の基底ではありません。単一量子ビットの場合、よく使われる基底は $\\class{plus-ket}{|{+}\\rangle}$ と $\\class{minus-ket}{|{-}\\rangle}$ というベクトルで形成されます。\n",
+        "\n",
+        "<!-- ::: column -->\n",
+        "\n",
+        "![同じ平面上の|0>, |1>基底と|+>, |->基底の両方を示す画像](images/quantum-states/basis.svg)\n",
+        "\n",
+        "<!-- ::: column -->\n",
+        "\n",
+        "$$ \\class{plus-ket}{|{+}\\rangle} = \\sqrt{\\tfrac{1}{2}} \\begin{bmatrix} \\class{_sq-amp0}{1} \\ \\class{_sq-amp1}{1} \\end{bmatrix} $$ $$ \\class{minus-ket}{|{-}\\rangle} = \\sqrt{\\tfrac{1}{2}} \\begin{bmatrix} \\class{_sq-amp0}{1} \\ \\class{_sq-amp1}{-1} \\end{bmatrix} $$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### 試してみよう\n",
+        "\n",
+        "これらの式が成り立つような $\\alpha$, $\\beta$, $\\gamma$, $\\delta$ の値を求めよ。\n",
+        "\n",
+        "- $\\alpha|{+}\\rangle + \\beta|{-}\\rangle = |0\\rangle$\n",
+        "- $\\gamma|{+}\\rangle + \\delta|{-}\\rangle = |1\\rangle$\n",
+        "\n",
+        "<!-- ::: -->"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "formulas": {
+          "_amp-i": {
+            "meaning": "'a<sub>i</sub>' is the amplitude of the state |i⟩, where |i⟩ is one of the computational basis states."
+          },
+          "sum": {
+            "meaning": "This means we add up the things on the right with different values of i, starting at i=0.",
+            "say": "'sum' or 'summation'. The character 'Σ' is capital <a href='https://en.wikipedia.org/wiki/Sigma'>sigma</a>."
+          }
+        },
+        "gloss": {
+          "matrix": {
+            "text": "Matrices are tables of numbers. They also come with some rules for adding and multiplying like vectors did. <a href='https://en.wikipedia.org/wiki/Matrix_(mathematics)'>Read more</a>.",
+            "title": "Matrix"
+          }
+        }
+      },
+      "source": [
+        "## 状態ベクトルは何種類あるのだろうか？\n",
+        "\n",
+        "We know that we can represent any quantum state using vectors, but is any vector a valid quantum state? In our case, no; since we square our amplitudes to find the probability of outcomes occurring, we need these squares to add to one, otherwise it doesn't make sense.\n",
+        "\n",
+        "$$ \\cssId{sum}{\\sum^{N-1}_{i=0}} \\cssId{_amp-i}{a_i}^2 = 1 $$\n",
+        "\n",
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### クイッククイズ\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"quiz2\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\n",
+        "Which of these is a valid quantum state? (Try adding up the squared amplitudes.)\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option(correct) -->\n",
+        "\n",
+        "1. $\\sqrt{\\tfrac{1}{3}}\\begin{bmatrix} 1 \\\\ -1 \\\\ 1 \\\\ 0 \\end{bmatrix}$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $\\sqrt{\\tfrac{1}{2}}\\begin{bmatrix} 1 \\\\ -1 \\\\ -1 \\\\ 1 \\end{bmatrix}$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $\\tfrac{1}{2}\\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix}$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "もう1つの要因は、状態ベクトルの「グローバル位相」と呼ばれるものです。位相が生む干渉効果によってしか位相の存在を検知できないので、私達は位相の*差*しか測定することが出来ません。もし、状態ベクトルのすべての振幅を同じだけ回転させたとしても、まったく同じ振る舞いが見られるでしょう。\n",
+        "\n",
+        "<!-- ::: column -->\n",
+        "\n",
+        "![異なる開始時の位相での干渉効果を示す画像](images/quantum-states/global-phase-L.svg)\n",
+        "\n",
+        "<!-- ::: column -->\n",
+        "\n",
+        "![異なる開始時の位相での干渉効果を示す画像](images/quantum-states/global-phase-R.svg)\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "例えば、この2つの状態を区別するような実験はできません。\n",
+        "\n",
+        "<!-- ::: column -->\n",
+        "\n",
+        "$$ |a\\rangle = \\sqrt{\\tfrac{1}{2}}\\begin{bmatrix} 1 \\ 0 \\ 0 \\ 1 \\end{bmatrix} $$\n",
+        "\n",
+        "<!-- ::: column -->\n",
+        "\n",
+        "$$ -|a\\rangle = \\sqrt{\\tfrac{1}{2}}\\begin{bmatrix} -1 \\ 0 \\ 0 \\ -1 \\end{bmatrix} $$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "なぜなら、それぞれの振幅の差は同じだからです。この2つのベクトルは*数学的には*異なるが*物理的には*同じと言えるでしょう。\n",
+        "\n",
+        "## 量子演算\n",
+        "\n",
+        "So now we know all about the different states our qubits can be in, it’s time to look at how we represent the operations that transform one state to another.\n",
+        "\n",
+        "In the same way there is a transition probability that a certain action will transform a coin from heads to tails, there is a transition amplitude for each starting state and end state of our qubits. We can describe any quantum operations through these transition amplitudes.\n",
+        "\n",
+        "![演算前後の2つの状態ベクトルを示す画像](images/quantum-states/quantum-operation.svg)\n",
+        "\n",
+        "So, what possible transformations are there? Say we have a starting state $|a\\rangle$ that’s transformed to a new state $|b\\rangle$. If we want our representation to cover every possible transformation, then each amplitude in $|a\\rangle$ must have a transition amplitude to each amplitude in $|b\\rangle$.\n",
+        "\n",
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### クイッククイズ\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"intro-describing-3\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\n",
+        "An $n$-qubit state vector can contain up to $2^n$ amplitudes. What’s the largest number of transition amplitudes we’d need to represent any quantum operation on $n$ qubits?\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $2\\cdot 2^n$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option(correct) -->\n",
+        "\n",
+        "1. $(2^n)^2$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $4^n$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $2^{2^n}$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "このように線を引くと、ちょっと面倒なので、代わりにこれらの数値をすべて[行列](gloss:matrix)に入れます。"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "formulas": {
+          "_cnot-gate": {
+            "meaning": "This is the label we have given the matrix that represents the CNOT gate."
+          },
+          "_t_amp_00_00": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>00</code> to <code>00</code>."
+          },
+          "_t_amp_00_01": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>00</code> to <code>01</code>."
+          },
+          "_t_amp_00_10": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>00</code> to <code>10</code>."
+          },
+          "_t_amp_00_11": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>00</code> to <code>11</code>."
+          },
+          "_t_amp_01_00": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>01</code> to <code>00</code>."
+          },
+          "_t_amp_01_01": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>01</code> to <code>01</code>."
+          },
+          "_t_amp_01_10": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>01</code> to <code>10</code>."
+          },
+          "_t_amp_01_11": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>01</code> to <code>11</code>."
+          },
+          "_t_amp_0_0": {
+            "meaning": "This is proportional to the transition amplitude of this operation transforming the state <code>0</code> to <code>0</code>."
+          },
+          "_t_amp_0_1": {
+            "meaning": "This is proportional to the transition amplitude of this operation transforming the state <code>0</code> to <code>1</code>."
+          },
+          "_t_amp_10_00": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>10</code> to <code>00</code>."
+          },
+          "_t_amp_10_01": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>10</code> to <code>01</code>."
+          },
+          "_t_amp_10_10": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>10</code> to <code>10</code>."
+          },
+          "_t_amp_10_11": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>10</code> to <code>11</code>."
+          },
+          "_t_amp_11_00": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>11</code> to <code>00</code>."
+          },
+          "_t_amp_11_01": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>11</code> to <code>01</code>."
+          },
+          "_t_amp_11_10": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>11</code> to <code>10</code>."
+          },
+          "_t_amp_11_11": {
+            "meaning": "This is the amplitude of this operation transforming the state <code>11</code> to <code>11</code>."
+          },
+          "_t_amp_1_0": {
+            "meaning": "This is proportional to the transition amplitude of this operation transforming the state <code>1</code> to <code>0</code>."
+          },
+          "_t_amp_1_1": {
+            "meaning": "This is proportional to the transition amplitude of this operation transforming the state <code>1</code> to <code>1</code>."
+          },
+          "dot": {
+            "meaning": "This dot is a shorthand for multiplication."
+          },
+          "u-gate": {
+            "meaning": "'U' is generally used to represent quantum gates, especially if the gate doesn't have a more specific name. It stands for 'unitary' which is something we'll learn about further down on this page."
+          }
+        },
+        "gloss": {
+          "cnot": {
+            "text": "The CNOT gate toggles the state of a 'target' qubit if the state of a 'control' qubit is 1.",
+            "title": "CNOT"
+          }
+        }
+      },
+      "source": [
+        "$$ \\cssId{u-gate}{U} = \\begin{bmatrix} \\class{*t_amp_00_00}{t*{00\\to 00}} &amp; \\class{*t_amp_01_00}{t*{01\\to 00}} &amp; \\class{*t_amp_10_00}{t*{10\\to 00}} &amp; \\class{*t_amp_11_00}{t*{11\\to 00}} \\ \\class{*t_amp_00_01}{t*{00\\to 01}} &amp; \\class{*t_amp_01_01}{t*{01\\to 01}} &amp; \\class{*t_amp_10_01}{t*{10\\to 01}} &amp; \\class{*t_amp_11_01}{t*{11\\to 01}} \\ \\class{*t_amp_00_10}{t*{00\\to 10}} &amp; \\class{*t_amp_01_10}{t*{01\\to 10}} &amp; \\class{*t_amp_10_10}{t*{10\\to 10}} &amp; \\class{*t_amp_11_10}{t*{11\\to 10}} \\ \\class{*t_amp_00_11}{t*{00\\to 11}} &amp; \\class{*t_amp_01_11}{t*{01\\to 11}} &amp; \\class{*t_amp_10_11}{t*{10\\to 11}} &amp; \\class{*t_amp_11_11}{t*{11\\to 11}} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "例えば、計算の原子で見たCNOT演算を表す行列は以下の通りです。\n",
+        "\n",
+        "$$ \\cssId{_cnot-gate}{\\text{CNOT}} = \\begin{bmatrix} \\class{_t_amp_00_00}{1} &amp; \\class{_t_amp_01_00}{0} &amp; \\class{_t_amp_10_00}{0} &amp; \\class{_t_amp_11_00}{0} \\ \\class{_t_amp_00_01}{0} &amp; \\class{_t_amp_01_01}{0} &amp; \\class{_t_amp_10_01}{0} &amp; \\class{_t_amp_11_01}{1} \\ \\class{_t_amp_00_10}{0} &amp; \\class{_t_amp_01_10}{0} &amp; \\class{_t_amp_10_10}{1} &amp; \\class{_t_amp_11_10}{0} \\ \\class{_t_amp_00_11}{0} &amp; \\class{_t_amp_01_11}{1} &amp; \\class{_t_amp_10_11}{0} &amp; \\class{_t_amp_11_11}{0} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### クイッククイズ\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"intro-maths-0\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\n",
+        "What is the transition amplitude of the CNOT operation (as shown above) transforming the state $|10\\rangle$ to $|01\\rangle$?\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $1$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option(correct) -->\n",
+        "\n",
+        "1. $0$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $\\begin{bmatrix} 1 &amp; 0 &amp; 0 &amp; 0\\end{bmatrix}$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. $\\begin{bmatrix} 0 \\\\ 0 \\\\ 1 \\\\ 0\\end{bmatrix}$\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "And here is the matrix for the H-gate we saw in the previous page:\n",
+        "\n",
+        "$$ H = \\sqrt{\\tfrac{1}{2}} \\begin{bmatrix} \\class{_t_amp_0_0}{1} &amp; \\class{_t_amp_1_0}{1} \\ \\class{_t_amp_0_1}{1} &amp; \\class{_t_amp_1_1}{-1} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "（行列とスカラーの掛け算は、ベクトルと同じルールを使います）。そして、ある操作がある量子ビットにどのような影響を与えるかを見たいときには、各遷移振幅を入力状態ベクトルの各状態の振幅に掛け、各状態の振幅を足して出力状態ベクトルとします。これは、確率（または振幅）木の各枝に沿って掛けて、最後に総確率（または振幅）を足し合わせるのと全く同じです。\n",
+        "\n",
+        "数学者の方ならおわかりかと思いますが、これは通常の行列の掛け算です。\n",
+        "\n",
+        "$$ H|0\\rangle = \\sqrt{\\tfrac{1}{2}} \\begin{bmatrix} \\class{_t_amp_0_0}{1} &amp; \\class{_t_amp_1_0}{ 1} \\ \\class{_t_amp_0_1}{1} &amp; \\class{_t_amp_1_1}{-1} \\ \\end{bmatrix} \\begin{bmatrix} \\class{_sq-amp0}{1} \\ \\class{_sq-amp1}{0} \\ \\end{bmatrix} = \\sqrt{\\tfrac{1}{2}} \\begin{bmatrix} (1 \\class{dot}{\\cdot} 1) &amp; + &amp;  (1 \\class{dot}{\\cdot} 0) \\ (1 \\class{dot}{\\cdot} 1) &amp; + &amp; (-1 \\class{dot}{\\cdot} 0) \\ \\end{bmatrix} = \\sqrt{\\tfrac{1}{2}} \\begin{bmatrix} \\class{_sq-amp0}{1} \\ \\class{_sq-amp1}{1} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "![Hゲートが状態|0>を状態|+>に変換する方法を示す画像](images/quantum-states/h-gate.svg)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 量子演算の規則\n",
+        "\n",
+        "すべてのベクトルが有効な状態ベクトルでないのと同じように、すべての行列が有効な量子演算であるわけではありません。もし行列が本当の演算として意味を持つなら、出力状態の合計確率を1に保つ必要があります。したがって、例えばこれは本当の演算にはなりえません。\n",
+        "\n",
+        "$$ \\begin{bmatrix} \\class{_t_amp_0_0}{1} &amp; \\class{_t_amp_1_0}{0} \\ \\class{_t_amp_0_1}{1} &amp; \\class{_t_amp_1_1}{0} \\ \\end{bmatrix} $$\n",
+        "\n",
+        "なぜなら、もしそれが状態 $|0\\rangle$ に作用するならば、次のようになるからです。\n",
+        "\n",
+        "# $$ \\begin{bmatrix} \\class{_t_amp_0_0}{1} &amp; \\class{_t_amp_1_0}{0} \\ \\class{_t_amp_0_1}{1} &amp; \\class{_t_amp_1_1}{0} \\ \\end{bmatrix}\\begin{bmatrix} 1 \\ 0 \\end{bmatrix}\n",
+        "\n",
+        "\\begin{bmatrix} \\class{_sq-amp0}{1} \\ \\class{_sq-amp1}{1} \\end{bmatrix} $$\n",
+        "\n",
+        "and the total probabilities add to two, which doesn't make any sense. Alternatively, if it acted on the state $|1\\rangle$, then the total probabilities would add up to zero, which also doesn't make sense. To preserve the total probability in all cases, our operations need to be reversible. This means we can perform our quantum gates backwards to 'undo' them (remembering to reverse any rotations) and be left with the state we started with. We say matrices with this property are *unitary*. You will often see quantum gates referred to as 'unitaries' or 'unitary gates'."
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 4
+}

From 1f0b193e13f9d6adf297c75925b9341c0a2858da Mon Sep 17 00:00:00 2001
From: Daiki Murata <d.murata0623@gmail.com>
Date: Wed, 8 Jun 2022 14:13:13 +0000
Subject: [PATCH 15/62] Translate describing-quantum-computers.ipynb via
 GitLocalize

---
 .../intro/describing-quantum-computers.ipynb  | 24 +++++++++----------
 1 file changed, 12 insertions(+), 12 deletions(-)

diff --git a/translations/ja/intro/describing-quantum-computers.ipynb b/translations/ja/intro/describing-quantum-computers.ipynb
index 6d579f0e5..a8edcf732 100644
--- a/translations/ja/intro/describing-quantum-computers.ipynb
+++ b/translations/ja/intro/describing-quantum-computers.ipynb
@@ -100,7 +100,7 @@
       "source": [
         "## 状態ベクトル\n",
         "\n",
-        "We saw in the last page that we can predict the behaviour of a quantum system by keeping track of the probability amplitudes for each outcome at each point in our computation. We also saw that, for n qubits, there are $2^n$ possible outcomes, and we can store these amplitudes in lists of length $2^n$ which we call vectors. Since these vectors describe the state of our qubits, we call them “state vectors”.\n",
+        "前ページでは、計算の各段階における各結果の確率振幅を記録することで、量子系の振る舞いを予測することができることを紹介しました。また、n個の量子ビットに対して、$2^n$ 個の可能な結果があり、これらの振幅を長さ $2^n$ のリストに格納することができることを確認しました。これらのベクトルは量子ビットの状態を表すので、私たちは「状態ベクトル」と呼んでいます。\n",
         "\n",
         "ここでは、2つの量子ビットを持つ量子コンピューターの状態ベクトルの例を示します。\n",
         "\n",
@@ -152,7 +152,7 @@
         "\n",
         "<!-- ::: .question -->\n",
         "\n",
-        "If the state vector above described the state of some qubits, what would be the *probability* of measuring ‘00’?\n",
+        "上の状態ベクトルがいくつかの量子ビットの状態を表しているとしたら、'00'を測定する*確率*はいくらか？\n",
         "\n",
         "<!-- ::: -->\n",
         "\n",
@@ -301,7 +301,7 @@
         "\n",
         "### 2つのベクトルを足し合わせる\n",
         "\n",
-        "The second rule is for adding two vectors together. This is only defined when the two vectors have the same number of elements, and gives a new vector with the same number of elements. Here is the general rule:\n",
+        "2つ目の規則は、2つのベクトルを足し合わせることです。これは、2つのベクトルが同じ要素数を持つ場合にのみ定義され、同じ要素数を持つ新しいベクトルが得られます。以下は一般的なルールです。\n",
         "\n",
         "$$ \\begin{bmatrix} \\class{_vec-el-0}{a_0} \\ \\class{_vec-el-1}{a_1} \\ \\class{_vec-el-2}{a_2} \\ \\class{_vec-el-3}{a_3} \\ \\class{dots}{\\vdots} \\ \\class{*vec-el-n}{a*{N-1}} \\ \\end{bmatrix} + \\begin{bmatrix} \\class{_vec-el-0}{b_0} \\ \\class{_vec-el-1}{b_1} \\ \\class{_vec-el-2}{b_2} \\ \\class{_vec-el-3}{b_3} \\ \\class{dots}{\\vdots} \\ \\class{*vec-el-n}{b*{N-1}} \\ \\end{bmatrix} \\class{equals}{=} \\begin{bmatrix} \\class{_vec-el-0}{a_0 + b_0} \\ \\class{_vec-el-1}{a_1 + b_1} \\ \\class{_vec-el-2}{a_2 + b_2} \\ \\class{<em data-md-type=\"emphasis\">vec-el-3}{a_3 + b_3} \\ \\class{dots}{\\vdots} \\ \\class{*vec-el-n}{a*{N-1} + b</em>{N-1}} \\ \\end{bmatrix} $$\n",
         "\n",
@@ -371,7 +371,7 @@
       "source": [
         "## 状態ベクトルは何種類あるのだろうか？\n",
         "\n",
-        "We know that we can represent any quantum state using vectors, but is any vector a valid quantum state? In our case, no; since we square our amplitudes to find the probability of outcomes occurring, we need these squares to add to one, otherwise it doesn't make sense.\n",
+        "我々は、ベクトルを使って任意の量子状態を表現できることは知っていますが、どんなベクトルでも正しい量子状態なのでしょうか？違います。というのも、出力の発生確率は振幅を二乗して求まるので、振幅の二乗和が1にならないと整合しないのです。\n",
         "\n",
         "$$ \\cssId{sum}{\\sum^{N-1}_{i=0}} \\cssId{_amp-i}{a_i}^2 = 1 $$\n",
         "\n",
@@ -383,7 +383,7 @@
         "\n",
         "<!-- ::: .question -->\n",
         "\n",
-        "Which of these is a valid quantum state? (Try adding up the squared amplitudes.)\n",
+        "この中で有効な量子状態はどれか？(振幅の2乗和を計算してみてください。）\n",
         "\n",
         "<!-- ::: -->\n",
         "\n",
@@ -437,13 +437,13 @@
         "\n",
         "## 量子演算\n",
         "\n",
-        "So now we know all about the different states our qubits can be in, it’s time to look at how we represent the operations that transform one state to another.\n",
+        "さて、量子ビットがとり得る様々な状態がわかったところで、ある状態から別の状態に変換する操作をどのように表現するかを見てみましょう。\n",
         "\n",
-        "In the same way there is a transition probability that a certain action will transform a coin from heads to tails, there is a transition amplitude for each starting state and end state of our qubits. We can describe any quantum operations through these transition amplitudes.\n",
+        "ある動作によってコインが表から裏へ変化する遷移確率があるように、量子ビットの始状態と終状態にはそれぞれ遷移振幅が存在するのです。この遷移振幅によって、任意の量子演算を記述することができます。\n",
         "\n",
         "![演算前後の2つの状態ベクトルを示す画像](images/quantum-states/quantum-operation.svg)\n",
         "\n",
-        "So, what possible transformations are there? Say we have a starting state $|a\\rangle$ that’s transformed to a new state $|b\\rangle$. If we want our representation to cover every possible transformation, then each amplitude in $|a\\rangle$ must have a transition amplitude to each amplitude in $|b\\rangle$.\n",
+        "では、どのような変換が可能なのでしょうか？例えば、始状態 $|a\\rangle$ があって、それが新しい状態 $|b\\rangle$ に変換されるとします。もし、私たちの表現がすべての可能な変換をカバーしたいのであれば、$|a\\rangle$ の各振幅は $|b\\rangle$ の各振幅への遷移振幅を持っている必要があります。\n",
         "\n",
         "<!-- ::: q-block.exercise -->\n",
         "\n",
@@ -453,7 +453,7 @@
         "\n",
         "<!-- ::: .question -->\n",
         "\n",
-        "An $n$-qubit state vector can contain up to $2^n$ amplitudes. What’s the largest number of transition amplitudes we’d need to represent any quantum operation on $n$ qubits?\n",
+        "$n$量子ビットの状態ベクトルは最大で $2^n$個の振幅を含むことができます。$n$量子ビットの量子演算を表現するために必要な遷移振幅の最大数値はいくつでしょう？\n",
         "\n",
         "<!-- ::: -->\n",
         "\n",
@@ -584,7 +584,7 @@
         "\n",
         "<!-- ::: .question -->\n",
         "\n",
-        "What is the transition amplitude of the CNOT operation (as shown above) transforming the state $|10\\rangle$ to $|01\\rangle$?\n",
+        "CNOT演算(上図)で状態 $|10\\rangle$ を $|01\\rangle$ に変換するときの遷移振幅は何でしょう？\n",
         "\n",
         "<!-- ::: -->\n",
         "\n",
@@ -616,7 +616,7 @@
         "\n",
         "<!-- ::: -->\n",
         "\n",
-        "And here is the matrix for the H-gate we saw in the previous page:\n",
+        "そして、前ページで見たHゲートの行列は以下になります。\n",
         "\n",
         "$$ H = \\sqrt{\\tfrac{1}{2}} \\begin{bmatrix} \\class{_t_amp_0_0}{1} &amp; \\class{_t_amp_1_0}{1} \\ \\class{_t_amp_0_1}{1} &amp; \\class{_t_amp_1_1}{-1} \\ \\end{bmatrix} $$\n",
         "\n",
@@ -646,7 +646,7 @@
         "\n",
         "\\begin{bmatrix} \\class{_sq-amp0}{1} \\ \\class{_sq-amp1}{1} \\end{bmatrix} $$\n",
         "\n",
-        "and the total probabilities add to two, which doesn't make any sense. Alternatively, if it acted on the state $|1\\rangle$, then the total probabilities would add up to zero, which also doesn't make sense. To preserve the total probability in all cases, our operations need to be reversible. This means we can perform our quantum gates backwards to 'undo' them (remembering to reverse any rotations) and be left with the state we started with. We say matrices with this property are *unitary*. You will often see quantum gates referred to as 'unitaries' or 'unitary gates'."
+        "となり、確率の合計は2になってしまい、整合しません。また、状態 $|1\\rangle$ に作用した場合、合計確率は0になり、これも整合しません。どのような場合でも確率の総和が変わらないようにするには、演算を可逆にする必要があります。つまり、量子ゲートを逆から実行して「元に戻す」ことができるのです（回転を反転させることを忘れずに）。このような性質を持つ行列を「ユニタリー行列」と呼びます。量子ゲートのことを「ユニタリー」または「ユニタリーゲート」と呼ぶのをよく見かけます。"
       ]
     }
   ],

From dd0022df819fd7d05627ab082ebbf596c5f05ea0 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Wed, 8 Jun 2022 16:32:29 +0200
Subject: [PATCH 16/62] modified styles of the gates

---
 frontend/vue/components/MiniComposer/Gate.vue | 18 ++++++++++++------
 1 file changed, 12 insertions(+), 6 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/Gate.vue b/frontend/vue/components/MiniComposer/Gate.vue
index bc5c2144a..c1f0cb905 100644
--- a/frontend/vue/components/MiniComposer/Gate.vue
+++ b/frontend/vue/components/MiniComposer/Gate.vue
@@ -67,7 +67,7 @@ export default class Gate extends Vue.with(Props) {
 .gate {
   width: 2rem;
   height: 2rem;
-  background-color: $red-50;
+  background-color: $teal-70;
   display: flex;
   align-content: center;
   align-items: center;
@@ -77,9 +77,10 @@ export default class Gate extends Vue.with(Props) {
   font-family: $plex-mono;
   font-style: normal;
   font-weight: normal;
-  font-size: 1.5rem;
+  font-size: 1.25rem;
   line-height: 1.25rem;
   text-align: center;
+  color: $text-color-white;
 
   &__symbol__rotation {
     font-size: 0.5rem;
@@ -92,17 +93,22 @@ export default class Gate extends Vue.with(Props) {
     }
   }
 
-  &_h {
-    background-color: $red-50;
+  &_h,
+  &_s {
+    background-color: $cyan-50;
+  }
+  &_t {
+    background-color: $purple-70;
   }
   &_z,
+  &_y,
   &_x {
-    background-color: $teal-40;
+    background-color: $teal-70;
   }
   &_rx,
   &_rz,
   &_ry {
-    background-color: $teal-40;
+    background-color: $teal-70;
     font-size: 1rem;
     line-height: 1rem;
   }

From cab79d6727e3dd0623f3091863d15316ffe19b63 Mon Sep 17 00:00:00 2001
From: Omar Costa Hamido <18335360+omarcostahamido@users.noreply.github.com>
Date: Wed, 8 Jun 2022 17:57:53 +0100
Subject: [PATCH 17/62] Update LOCALIZATION_CONTRIBUTORS

- add OCH to localization contributors
- propose `PT_UN` as in PT-PT + PT-BR
---
 LOCALIZATION_CONTRIBUTORS | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/LOCALIZATION_CONTRIBUTORS b/LOCALIZATION_CONTRIBUTORS
index e1d6b85cf..a6dcfb51a 100644
--- a/LOCALIZATION_CONTRIBUTORS
+++ b/LOCALIZATION_CONTRIBUTORS
@@ -49,10 +49,11 @@ Indonesian (ID)
 Hanifan Rizki Nurahman | Hanifanrn
 Natasha Valentina | natashaval
 
-Portuguese (PT)
+Portuguese (PT_UN)
 
 Gustavo Mirapalheta | gustavomirapalheta
 Marco Antonio Barroca | MarcoBarroca
+Omar Costa Hamido | omarcostahamido
 
 Simplified Chinese (ZH-CHS)
 

From 36bb3fe0b95a358ad046e6ab56ba6846c6223c75 Mon Sep 17 00:00:00 2001
From: Omar Costa Hamido <18335360+omarcostahamido@users.noreply.github.com>
Date: Wed, 8 Jun 2022 18:03:13 +0100
Subject: [PATCH 18/62] Update LOCALIZATION_CONTRIBUTORS

undo
---
 LOCALIZATION_CONTRIBUTORS | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/LOCALIZATION_CONTRIBUTORS b/LOCALIZATION_CONTRIBUTORS
index a6dcfb51a..fc064ee8f 100644
--- a/LOCALIZATION_CONTRIBUTORS
+++ b/LOCALIZATION_CONTRIBUTORS
@@ -49,7 +49,7 @@ Indonesian (ID)
 Hanifan Rizki Nurahman | Hanifanrn
 Natasha Valentina | natashaval
 
-Portuguese (PT_UN)
+Portuguese (PT)
 
 Gustavo Mirapalheta | gustavomirapalheta
 Marco Antonio Barroca | MarcoBarroca

From b417c11f2fbafac64e38e89c488ad97e4beea7b1 Mon Sep 17 00:00:00 2001
From: Omar Costa Hamido <18335360+omarcostahamido@users.noreply.github.com>
Date: Wed, 8 Jun 2022 18:05:31 +0100
Subject: [PATCH 19/62] Update LOCALIZATION_CONTRIBUTORS

- propose `PT_UN` as in `PT-PT` + `PT-BR`, similar to what happened to `ES_UN` here, and in crowdin/[qiskit-docs](https://github.com/qiskit-community/qiskit-translations/blob/master/LOCALIZATION_CONTRIBUTORS) as well.
---
 LOCALIZATION_CONTRIBUTORS | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/LOCALIZATION_CONTRIBUTORS b/LOCALIZATION_CONTRIBUTORS
index e1d6b85cf..59ea20c69 100644
--- a/LOCALIZATION_CONTRIBUTORS
+++ b/LOCALIZATION_CONTRIBUTORS
@@ -49,7 +49,7 @@ Indonesian (ID)
 Hanifan Rizki Nurahman | Hanifanrn
 Natasha Valentina | natashaval
 
-Portuguese (PT)
+Portuguese (PT_UN)
 
 Gustavo Mirapalheta | gustavomirapalheta
 Marco Antonio Barroca | MarcoBarroca

From 5cf2a77823658d4ab0af60743322c6b0a5845dc5 Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Nat=C3=A1lia=20Capra=20Ferrazzo?=
 <nataliaferrazzo@hotmail.com>
Date: Wed, 8 Jun 2022 14:27:38 -0300
Subject: [PATCH 20/62] Update LOCALIZATION_CONTRIBUTORS

---
 LOCALIZATION_CONTRIBUTORS | 1 +
 1 file changed, 1 insertion(+)

diff --git a/LOCALIZATION_CONTRIBUTORS b/LOCALIZATION_CONTRIBUTORS
index e1d6b85cf..09d927799 100644
--- a/LOCALIZATION_CONTRIBUTORS
+++ b/LOCALIZATION_CONTRIBUTORS
@@ -53,6 +53,7 @@ Portuguese (PT)
 
 Gustavo Mirapalheta | gustavomirapalheta
 Marco Antonio Barroca | MarcoBarroca
+Natália Capra Ferrazzo | nataliaferrazzo
 
 Simplified Chinese (ZH-CHS)
 

From 3feab9257b021221e7291062b099252c457cefde Mon Sep 17 00:00:00 2001
From: =?UTF-8?q?Andr=C3=A9=20Galdino=20dos=20Santos?=
 <79878419+andregs2709@users.noreply.github.com>
Date: Wed, 8 Jun 2022 14:43:09 -0300
Subject: [PATCH 21/62] Update LOCALIZATION_CONTRIBUTORS

---
 LOCALIZATION_CONTRIBUTORS | 1 +
 1 file changed, 1 insertion(+)

diff --git a/LOCALIZATION_CONTRIBUTORS b/LOCALIZATION_CONTRIBUTORS
index e1d6b85cf..2defb297e 100644
--- a/LOCALIZATION_CONTRIBUTORS
+++ b/LOCALIZATION_CONTRIBUTORS
@@ -53,6 +53,7 @@ Portuguese (PT)
 
 Gustavo Mirapalheta | gustavomirapalheta
 Marco Antonio Barroca | MarcoBarroca
+André Galdino dos Santos | andregs2709
 
 Simplified Chinese (ZH-CHS)
 

From 41a12b248deb7c0402e845f47cd645575318a985 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Wed, 8 Jun 2022 20:30:12 +0200
Subject: [PATCH 22/62] corrected tex visualization

---
 .../vue/components/MiniComposer/gateUtils.ts  | 49 ++++++++-----------
 1 file changed, 20 insertions(+), 29 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/gateUtils.ts b/frontend/vue/components/MiniComposer/gateUtils.ts
index a5f621be3..0411832c0 100644
--- a/frontend/vue/components/MiniComposer/gateUtils.ts
+++ b/frontend/vue/components/MiniComposer/gateUtils.ts
@@ -1,5 +1,5 @@
 // eslint-disable-next-line import/named
-import { multiply, subtract, add, gcd, flatten, map, round } from 'mathjs'
+import { multiply, subtract, add, gcd, round } from 'mathjs'
 
 export enum GateName {
   UNKNOWN = 'UNKNOWN',
@@ -27,20 +27,6 @@ export interface StateMatrix {
   m: number
 }
 
-function reduce (state: StateMatrix) {
-  const { A, B, C, D, m } = state
-  const matricesValues = flatten([...A, ...B, ...C, ...D]) as unknown as number[]
-  const d = gcd(...matricesValues, Math.pow(2, m))
-
-  return {
-    A: map(A, value => round(value / d)),
-    B: map(B, value => round(value / d)),
-    C: map(C, value => round(value / d)),
-    D: map(D, value => round(value / d)),
-    m: round(m / d)
-  }
-}
-
 function reduceSingleElement (numerator: number, denominator: number) {
   const d = gcd(numerator, denominator)
 
@@ -74,13 +60,13 @@ export const XGate: QuantumGate = {
   apply (state: StateMatrix) {
     // Integer part
     const K = [[0, 1], [1, 0]]
-    return reduce({
+    return {
       A: multiply(K, state.A),
       B: multiply(K, state.B),
       C: multiply(K, state.C),
       D: multiply(K, state.D),
       m: state.m
-    })
+    }
   }
 }
 
@@ -89,13 +75,13 @@ export const YGate: QuantumGate = {
     // Integer part
     const K = [[0, -1], [1, 0]]
 
-    return reduce({
+    return {
       A: neg(multiply(K, state.B)),
       B: multiply(K, state.A),
       C: neg(multiply(K, state.D)),
       D: multiply(K, state.C),
       m: state.m
-    })
+    }
   }
 }
 
@@ -104,13 +90,13 @@ export const ZGate: QuantumGate = {
     // Integer part
     const K = [[1, 0], [0, -1]]
 
-    return reduce({
+    return {
       A: multiply(K, state.A),
       B: multiply(K, state.B),
       C: multiply(K, state.C),
       D: multiply(K, state.D),
       m: state.m
-    })
+    }
   }
 }
 
@@ -119,13 +105,13 @@ export const HGate: QuantumGate = {
     // Integer part
     const K = [[1, 1], [1, -1]]
 
-    return reduce({
+    return {
       A: multiply(multiply(K, state.C), 2),
       B: multiply(multiply(K, state.D), 2),
       C: multiply(K, state.A),
       D: multiply(K, state.B),
       m: state.m + 1
-    })
+    }
   }
 }
 
@@ -135,13 +121,13 @@ export const SGate: QuantumGate = {
     const K1 = [[1, 0], [0, 0]]
     const K2 = [[0, 0], [0, 1]]
 
-    return reduce({
+    return {
       A: subtract(multiply(K1, state.A), multiply(K2, state.B)),
       B: add(multiply(K2, state.A), multiply(K1, state.B)),
       C: subtract(multiply(K1, state.C), multiply(K2, state.D)),
       D: add(multiply(K2, state.C), multiply(K1, state.D)),
       m: state.m
-    })
+    }
   }
 }
 
@@ -164,13 +150,13 @@ export const TGate: QuantumGate = {
     const K2_C_2 = multiply(K2_C, 2)
     const K2_D_2 = multiply(K2_D, 2)
 
-    return reduce({
+    return {
       A: subtract(add(K1_A, K2_C_2), K2_D_2),
       B: add(add(K1_B, K2_C_2), K2_D_2),
       C: add(subtract(K2_A, K2_B), K1_C),
       D: add(add(K2_A, K2_B), K1_D),
       m: state.m + 1
-    })
+    }
   }
 }
 
@@ -205,7 +191,7 @@ function signedString (n: number, m: number, symbol: string = '') {
     numeratorTex = `${absNumerator}`
   }
 
-  if (m > 0) {
+  if (denominator !== 1 && m > 0) {
     return `${sign}\\frac{${numeratorTex}}{${denominator}}`
   } else {
     return `${sign}${numeratorTex}`
@@ -221,7 +207,12 @@ function StateMatrixElementToTex (state: StateMatrix, coords: { x: number, y: nu
     return '0'
   }
 
-  let tex = `${signedString(a, state.m)}${signedString(b, state.m, 'i')}${signedString(c, state.m, '\\sqrt{2}')}${signedString(d, state.m, 'i\\sqrt{2}')}`
+  const aTex = signedString(a, state.m)
+  const bTex = signedString(b, state.m, 'i')
+  const cTex = signedString(c, state.m, '\\sqrt{2}')
+  const dTex = signedString(d, state.m, 'i\\sqrt{2}')
+
+  let tex = `${aTex}${bTex}${cTex}${dTex}`
 
   if (tex.startsWith('+')) {
     tex = tex.substring(1)

From 83568fea127ee99228c02b219dcd78527ecac814 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Wed, 8 Jun 2022 20:31:28 +0200
Subject: [PATCH 23/62] limited number of gates

---
 frontend/vue/components/MiniComposer/Circuit.vue   |  2 ++
 .../MiniComposer/CircuitSandboxWidget.vue          |  2 ++
 frontend/vue/components/MiniComposer/GatesPool.vue | 10 ++++++++--
 frontend/vue/components/MiniComposer/QubitLine.vue | 14 +++++++++++---
 4 files changed, 23 insertions(+), 5 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/Circuit.vue b/frontend/vue/components/MiniComposer/Circuit.vue
index 745878f19..a2023c188 100644
--- a/frontend/vue/components/MiniComposer/Circuit.vue
+++ b/frontend/vue/components/MiniComposer/Circuit.vue
@@ -5,6 +5,7 @@
       :key="index"
       :circuit-state="qubitLine"
       :auto-measure-gate="autoMeasureGate"
+      :max-gates="maxGates"
       @onGatesChanged="OnGatesChanged"
     />
     <button
@@ -30,6 +31,7 @@ class Props {
   circuitState = prop<ComposerGate[][]>({ default: [[]], required: true })
   autoMeasureGate = prop<boolean>({ default: true, required: true })
   maxLines = prop<Number>({ default: 1, required: true })
+  maxGates = prop<Number>({ default: -1, required: true })
 }
 
 @Options({
diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index 7d1a73ade..a493ba6a4 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -24,6 +24,7 @@
         :circuit-state="circuitState"
         :auto-measure-gate="autoMeasureGate"
         :max-lines="circuitState.length"
+        :max-gates="MAX_GATES"
       />
     </div>
     <div class="mini-composer__state-views">
@@ -89,6 +90,7 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   lessonRef = ref<HTMLDivElement | null>(null)
   get lessonDiv () { return (this.lessonRef as unknown as HTMLDivElement) }
 
+  MAX_GATES = 7
   correctSolution = SolutionState.CORRECT
 
   autoMeasureGate: boolean = false
diff --git a/frontend/vue/components/MiniComposer/GatesPool.vue b/frontend/vue/components/MiniComposer/GatesPool.vue
index 35c548fbb..c658903d6 100644
--- a/frontend/vue/components/MiniComposer/GatesPool.vue
+++ b/frontend/vue/components/MiniComposer/GatesPool.vue
@@ -3,7 +3,7 @@
     class="gates-pool"
     :list="availableGates"
     :move="onMoveCallback"
-    group="people"
+    group="gates"
     item-key="name"
     @change="log"
   >
@@ -37,7 +37,13 @@ class Props {
   }
 })
 export default class CircuitLine extends Vue.with(Props) {
-
+  onMoveCallback (evt : any) {
+    const dropTarget: HTMLElement = evt?.to
+    if (!dropTarget) {
+      return true
+    }
+    return !dropTarget.classList.contains('qubit-line__slot__full')
+  }
 }
 </script>
 <style scoped lang="scss">
diff --git a/frontend/vue/components/MiniComposer/QubitLine.vue b/frontend/vue/components/MiniComposer/QubitLine.vue
index 7883c99fe..9ac992db8 100644
--- a/frontend/vue/components/MiniComposer/QubitLine.vue
+++ b/frontend/vue/components/MiniComposer/QubitLine.vue
@@ -4,10 +4,10 @@
     <div class="qubit-line__slot-container">
       <draggable
         class="qubit-line__slot"
-        :list="circuitState"
-        :move="onMoveCallback"
-        group="people"
+        :class="{'qubit-line__slot__full': isFull}"
+        group="gates"
         item-key="name"
+        :list="circuitState"
         @change="log"
       >
         <template #item="{ element }">
@@ -35,6 +35,7 @@ class Props {
   name = prop<GateName>({ default: GateName.H, required: true })
   circuitState = prop<ComposerGate[]>({ default: [], required: true })
   autoMeasureGate = prop<boolean>({ default: true, required: true })
+  maxGates = prop<Number>({ default: -1, required: true })
 }
 
 @Options({
@@ -51,6 +52,13 @@ export default class QubitLine extends Vue.with(Props) {
   log () {
     this.$emit('onGatesChanged')
   }
+
+  get isFull () {
+    if (this.maxGates === -1) {
+      return false
+    }
+    return this.circuitState.length >= this.maxGates
+  }
 }
 </script>
 

From 96eb84bfde177c0815599670e22d0d1a5750ae23 Mon Sep 17 00:00:00 2001
From: Soyoung Shin <sophy.shin@kakao.com>
Date: Thu, 9 Jun 2022 11:39:16 +0000
Subject: [PATCH 24/62] Translate bernstein-vazirani.ipynb via GitLocalize

---
 .../ko/ch-algorithms/bernstein-vazirani.ipynb | 646 ++++++++++++++++++
 1 file changed, 646 insertions(+)
 create mode 100644 translations/ko/ch-algorithms/bernstein-vazirani.ipynb

diff --git a/translations/ko/ch-algorithms/bernstein-vazirani.ipynb b/translations/ko/ch-algorithms/bernstein-vazirani.ipynb
new file mode 100644
index 000000000..1462fb17e
--- /dev/null
+++ b/translations/ko/ch-algorithms/bernstein-vazirani.ipynb
@@ -0,0 +1,646 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "tags": [
+          "remove_cell"
+        ]
+      },
+      "source": [
+        "# Bernstein-Vazirani 알고리즘"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "이 섹션에서는 먼저 Bernstein-Vazirani 문제와 그 고전적 솔루션 및 이 문제를 해결하기 위한 양자 알고리즘을 소개합니다. 그런 다음 Qiskit을 사용하여 양자 알고리즘을 구현하고 시뮬레이터와 실제 양자 백엔드 모두에서 실행해 보겠습니다."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 1. Bernstein-Vazirani 알고리즘<a id=\"algorithm\"></a>\n",
+        "\n",
+        "Reference [1]에서 처음 소개된 Bernstein-Vazirani 알고리즘은 지난 섹션에서 다룬 Deutsch-Jozsa 알고리즘의 확장으로 볼 수 있습니다. Deutsch-Jozsa 문제보다 더 복잡한 문제의 해결에 양자 컴퓨터를 사용하면 이점이 있을 수 있음을 보여주었습니다.\n",
+        "\n",
+        "### 1.1  Bernstein-Vazirani 문제<a id=\"bvproblem\"> </a>\n",
+        "\n",
+        "다시 입력으로 비트 문자열($x$)을 사용하고 $0$ 또는 $1$를 반환하는 블랙박스 함수 $f$가 제공됩니다. 즉 $$f({x_0,x_1,x_2, ...}) \\rightarrow 0 \\textrm{ or } 1 \\textrm{ where } x_n \\textrm{ is }0 \\textrm{ or } 1 $$입니다.\n",
+        "\n",
+        "Deutsch-Jozsa 문제처럼  함수가 상수 함수이거나 균형 함수인 것이 아니라, 이제 함수는 문자열 $s$에 따라 입력의 비트 곱을 반환하게 됩니다. 즉, 입력 $x$, $f(x) = s \\cdot x , \\text{(mod 2)}$가 주어지며 $s$를 찾아내야 합니다. 고전적인 가역 회로로서 Bernstein-Vazirani 오라클은 다음과 같습니다.\n",
+        "\n",
+        "![고전적인 가역 회로](images/bv2.png)\n",
+        "\n",
+        "### 1.2 고전적 해법<a id=\"classical-solution\"> </a>\n",
+        "\n",
+        "일반적으로 오라클은 $$f_s(x) = s \\cdot x \\mod 2$$를 입력하면 $x$를 반환합니다. 따라서 숨겨진 비트 문자열 $s$는 여러가지 입력값들로 오라클을 탐색하여 드러낼 수 있습니다.\n",
+        "\n",
+        "Input(x)\n",
+        ":-:\n",
+        "100...0\n",
+        "010...0\n",
+        "001...0\n",
+        "000...1\n",
+        "\n",
+        "여기서 각 쿼리는 $s$의 서로 다른 비트($s_i$ 비트)를 나타냅니다. 예를 들어 `x = 1000...0` 일 때 $s$의 최하위 비트를 얻을 수 있고 `x = 0100...0` 일 때 다음 최하위 비트를 찾을 수 있는 방식입니다. 따라서 $f_s(x)$ 함수를 $n$ 번 호출해야 한다는 것을 의미합니다. "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 1.3 양자 솔루션<a id=\"quantum-solution\"> </a>\n",
+        "\n",
+        "양자 컴퓨터를 사용하면 $f(x)$ 함수를 한 번만 호출하면 100% 확실하게이 문제를 해결할 수 있습니다. 숨겨진 비트 문자열을 찾는 양자 Bernstein-Vazirani 알고리즘은 매우 간단합니다.\n",
+        "\n",
+        "1. 입력 큐비트를 $|0\\rangle^{\\otimes n}$ 상태로 초기화하고 출력 큐비트를 $|{-}\\rangle$로 초기화합니다.\n",
+        "2. 입력 레지스터에 Hadamard 게이트 적용\n",
+        "3. 오라클 탐색\n",
+        "4. 입력 레지스터에 Hadamard 게이트 적용\n",
+        "5. 측정\n",
+        "\n",
+        "<img src=\"images/bv1.png\" alt=\"Bernstein-Vazirani 양자 회로\">\n",
+        "\n",
+        "알고리즘을 설명하기 위해 각 큐비트에 H-게이트를 적용할 때 어떤 일이 발생하는지 더 자세히 살펴보겠습니다. $n$-큐비트 $|a\\rangle$인 상태에 H-gate를 적용하고 어떤 변환이 일어나는지 살펴봅시다.\n",
+        "\n",
+        "$$ |a\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^ {a\\cdot x}|x\\rangle. $$\n",
+        "\n",
+        "<details>\n",
+        "    <summary>방정식 설명(확대하려면 클릭)</summary>\n",
+        "</details>\n",
+        "\n",
+        " 우리는 Hadamard가 하나의 큐비트에서 다음 변환을 수행한다는 것을 기억합니다.\n",
+        "\n",
+        "$$ H|0\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) $$ $$ H|1\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle) $$\n",
+        "\n",
+        "합 표기을 사용하여 다음과 같이 다시 작성할 수 있습니다.\n",
+        "\n",
+        "$$ H|a\\rangle = \\frac{1}{\\sqrt{2}}\\sum_{x\\in {0,1}} (-1)^{a\\cdot x}|x\\rangle. $$\n",
+        "\n",
+        "두 개의 큐비트에 대해 각각에 Hadamard를 적용하면 다음 변환이 수행됩니다.\n",
+        "\n",
+        "$$ H^{\\otimes 2}|00\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle) $$ $$ H^{\\otimes 2}|01\\rangle = \\tfrac{1}{2}(|00\\rangle - |01\\rangle + |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}|10\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle - |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}|11\\rangle = \\tfrac{1}{2}(|00\\rangle - |01\\rangle - |10\\rangle + |11\\rangle) $$\n",
+        "\n",
+        "합을 사용하여 아래와 같이 표현할 수 있습니다.\n",
+        "\n",
+        "$$ H^{\\otimes 2}|a\\rangle = \\frac{1}{2}\\sum_{x\\in {0,1}^2} (-1)^{a\\cdot x}|x\\rangle $$\n",
+        "\n",
+        "이제 위의 수식을 도출해 보도록 합시다.\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "특히, 양자 레지스터 $|00\\dots 0\\rangle$ 상태로 시작하여 $n$ Hadamard 게이트를 적용하면 익숙한 양자 중첩 상태를 얻게 됩니다.\n",
+        "\n",
+        "$$ |00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} |x\\rangle $$\n",
+        "\n",
+        "이 경우 $a=0$이므로 위상 항 $(-1)^{a\\cdot x}$는 사라집니다. 따라서 $(-1)^{a\\cdot x} = 1$입니다.\n",
+        "\n",
+        "고전적 오라클 $f_s$는 $s \\cdot x\\mod 2 = 1$인 입력 $x$에 대해 $1$를 반환하고 그렇지 않으면 $0$를 반환합니다. Deutsch-Jozsa 알고리즘처럼 위상 반동 기법을 사용하고 $|{-}\\rangle$ 상태의 큐비트에 대해 적용하면 다음 변환을 얻습니다.\n",
+        "\n",
+        "$$ |x \\rangle \\xrightarrow{f_s} (-1)^{s\\cdot x} |x \\rangle $$\n",
+        "\n",
+        "숨겨진 비트 문자열을 드러내는 알고리즘은 $|00\\dots 0\\rangle$의 Hadamard 변환에서 얻은 양자 중첩으로 양자 오라클 $f_s$를 쿼리하여 얻어집니다. 즉,\n",
+        "\n",
+        "$$ |00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} |x\\rangle \\xrightarrow{f_a} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^{a\\cdot x}|x\\rangle $$\n",
+        "\n",
+        "$n$ Hadamard 게이트의 역수는 다시 $n$ Hadamard 게이트이므로 $a$를 얻을 수 있습니다.\n",
+        "\n",
+        "$$ \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^{a\\cdot x}|x\\rangle \\xrightarrow{H^{\\otimes n}} |a\\rangle $$"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 2. 예제<a id=\"example\"></a>\n",
+        "\n",
+        "$n=2$ 큐비트와 숨겨진 문자열 $s=11$에 대한 구체적인 예를 살펴보겠습니다. 단 하나의 레지스터를 사용하여 Bernstein-Vazirani 양자 오라클 회로를 생성 과정은 참조 [2]의 공식을 따르고 있음에 유의하십시오.\n",
+        "\n",
+        "<ol>\n",
+        "    <li>두 큐비트의 레지스터는 0으로 초기화됩니다.</li>\n",
+        "</ol>\n",
+        "\n",
+        "$$\\lvert \\psi_0 \\rangle = \\lvert 0 0 \\rangle$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>두 큐비트에 Hadamard 게이트를 적용합니다.</li>\n",
+        "\n",
+        "\n",
+        "$$\\lvert \\psi_1 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle + \\lvert 0 1 \\rangle + \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right) $$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>$s=11$ 문자열에 대해 양자 오라클은 $$ |x \\rangle \\xrightarrow{f_s} (-1)^{x\\cdot 11} |x \\rangle$$ 연산을 수행합니다.</li>\n",
+        "\n",
+        "\n",
+        "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( (-1)^{00\\cdot 11}|00\\rangle + (-1)^{01\\cdot 11}|01\\rangle + (-1)^{10\\cdot 11}|10\\rangle + (-1)^{11\\cdot 11}|11\\rangle \\right)$$\n",
+        "\n",
+        "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle - \\lvert 0 1 \\rangle - \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>두 큐비트에 Hadamard 게이트를 적용합니다.</li>\n",
+        "\n",
+        "\n",
+        "$$\\lvert \\psi_3 \\rangle = \\lvert 1 1 \\rangle$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>숨겨진 문자열 $s=11$을 찾기 위한 측정</li>\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "아래 `bv_widget` 위젯을 사용합니다. 버튼을 눌러 다른 과정을 적용하고 알고리즘을 따라해 보십시오. 첫 두 개의 인수를 사용해 입력 큐비트 수와 숨겨진 문자열의 값을 변경할 수 있습니다."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 1,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "4738e4d9713a4204bfa2df6c5179fe2b",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "HBox(children=(Button(description='H⊗ⁿ', style=ButtonStyle()), Button(description='Oracle', style=ButtonStyle(…"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        },
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "aee1e515e0714a978b73ad1fd332945a",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "HTMLMath(value='$$ |00\\\\rangle = |00\\\\rangle $$')"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        },
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "0392b76bb3674157aa5c1f8d0836ec3e",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "Image(value=b'\\x89PNG\\r\\n\\x1a\\n\\x00\\x00\\x00\\rIHDR\\x00\\x00\\x00\\xce\\x00\\x00\\x00\\xcc\\x08\\x06\\x00\\x00\\x00;\\xd7\\x9c…"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "from qiskit_textbook.widgets import bv_widget\n",
+        "bv_widget(2, \"11\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 3. Qiskit 구현<a id=\"implementation\"></a>\n",
+        "\n",
+        "이제 $s=011$인 3비트 함수에 대한 Qiskit의 Bernstein-Vazirani 알고리즘 구현을 살펴보겠습니다."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 2,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "# initialization\n",
+        "import matplotlib.pyplot as plt\n",
+        "import numpy as np\n",
+        "\n",
+        "# importing Qiskit\n",
+        "from qiskit import IBMQ, Aer\n",
+        "from qiskit.providers.ibmq import least_busy\n",
+        "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, transpile\n",
+        "\n",
+        "# import basic plot tools\n",
+        "from qiskit.visualization import plot_histogram"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "먼저 실험에 사용될 큐비트의 수와 알고리즘에서 찾을 숨겨진 비트 문자열 $s$를 설정합니다. 숨겨진 비트 문자열 $s$는 양자 오라클의 회로를 결정합니다. "
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 3,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "n = 3 # number of qubits used to represent s\n",
+        "s = '011'   # the hidden binary string"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "그런 다음 Qiskit을 사용하여 Bernstein-Vazirani 알고리즘을 프로그래밍합니다."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 4,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "image/svg+xml": [
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+            ],
+            "text/plain": [
+              "<Figure size 748.797x325.08 with 1 Axes>"
+            ]
+          },
+          "execution_count": 4,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# We need a circuit with n qubits, plus one auxiliary qubit\n",
+        "# Also need n classical bits to write the output to\n",
+        "bv_circuit = QuantumCircuit(n+1, n)\n",
+        "\n",
+        "# put auxiliary in state |->\n",
+        "bv_circuit.h(n)\n",
+        "bv_circuit.z(n)\n",
+        "\n",
+        "# Apply Hadamard gates before querying the oracle\n",
+        "for i in range(n):\n",
+        "    bv_circuit.h(i)\n",
+        "    \n",
+        "# Apply barrier \n",
+        "bv_circuit.barrier()\n",
+        "\n",
+        "# Apply the inner-product oracle\n",
+        "s = s[::-1] # reverse s to fit qiskit's qubit ordering\n",
+        "for q in range(n):\n",
+        "    if s[q] == '0':\n",
+        "        bv_circuit.i(q)\n",
+        "    else:\n",
+        "        bv_circuit.cx(q, n)\n",
+        "        \n",
+        "# Apply barrier \n",
+        "bv_circuit.barrier()\n",
+        "\n",
+        "#Apply Hadamard gates after querying the oracle\n",
+        "for i in range(n):\n",
+        "    bv_circuit.h(i)\n",
+        "\n",
+        "# Measurement\n",
+        "for i in range(n):\n",
+        "    bv_circuit.measure(i, i)\n",
+        "\n",
+        "bv_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 3a. 시뮬레이터 실험<a id=\"simulation\"></a>\n",
+        "\n",
+        "시뮬레이터를 사용해 위의 회로를 실행해 봅시다. "
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 5,
+      "metadata": {
+        "scrolled": false
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 5,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# use local simulator\n",
+        "aer_sim = Aer.get_backend('aer_simulator')\n",
+        "shots = 1024\n",
+        "results = aer_sim.run(bv_circuit).result()\n",
+        "answer = results.get_counts()\n",
+        "\n",
+        "plot_histogram(answer)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "측정 결과가 숨겨진 문자열 `011` 임을 알 수 있습니다. "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 3b. 실제 양자 백엔드로 실험<a id=\"device\"></a>\n",
+        "\n",
+        "아래와 같이 실제 장치에서 회로를 실행할 수 있습니다."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 6,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ]
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "least busy backend:  ibmq_quito\n"
+          ]
+        }
+      ],
+      "source": [
+        "# Load our saved IBMQ accounts and get the least busy backend device with less than or equal to 5 qubits\n",
+        "IBMQ.load_account()\n",
+        "provider = IBMQ.get_provider(hub='ibm-q')\n",
+        "provider.backends()\n",
+        "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits <= 5 and\n",
+        "                                   x.configuration().n_qubits >= 2 and\n",
+        "                                   not x.configuration().simulator and x.status().operational==True))\n",
+        "print(\"least busy backend: \", backend)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 7,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ]
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Job Status: job has successfully run\n"
+          ]
+        }
+      ],
+      "source": [
+        "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n",
+        "from qiskit.tools.monitor import job_monitor\n",
+        "\n",
+        "shots = 1024\n",
+        "transpiled_bv_circuit = transpile(bv_circuit, backend)\n",
+        "job = backend.run(transpiled_bv_circuit, shots=shots)\n",
+        "\n",
+        "job_monitor(job, interval=2)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 8,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ]
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 8,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# Get the results from the computation\n",
+        "results = job.result()\n",
+        "answer = results.get_counts()\n",
+        "\n",
+        "plot_histogram(answer)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "보시다시피 가장 높은 확률의 결과는 `011` 입니다. 다른 결들은 양자 계산의 에러로 인한 것입니다. "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 4. 연습 <a id=\"problems\"></a>\n",
+        "\n",
+        "1. 아래 위젯을 사용하여 다양한 오라클에서 작동하는 Bernstein-Vazirani 알고리즘을 확인해 보십시오."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 9,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "50aab689dcab494488d8ca5be416d30e",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "HBox(children=(Button(description='H⊗ⁿ', style=ButtonStyle()), Button(description='Oracle', style=ButtonStyle(…"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        },
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "9de25e0347754d70a79689270d19b1bb",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "HTMLMath(value='$$ |000\\\\rangle = |000\\\\rangle $$')"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        },
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "d34999a9c17949b4ac75bb46bc01c603",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "Image(value=b'\\x89PNG\\r\\n\\x1a\\n\\x00\\x00\\x00\\rIHDR\\x00\\x00\\x00\\xce\\x00\\x00\\x01\\x08\\x08\\x06\\x00\\x00\\x00\\x17\\xd9\\…"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "from qiskit_textbook.widgets import bv_widget\n",
+        "bv_widget(3, \"011\", hide_oracle=False)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "1. 위의 Bernstein-Vazirani 알고리즘의 [구현](#implementation) 은 숨겨진 비트 문자열 $s = 011$에 대한 것입니다. 숨겨진 문자열 $s = 1011$에 대하여 수정해서 구현해 봅시다. 결과가 예상대로입니까? 설명해 봅시다.\n",
+        "2. 위의 Bernstein-Vazirani 알고리즘의 [구현](#implementation) 은 숨겨진 비트 문자열 $s = 011$에 대한 것입니다. 숨겨진 문자열 $s = 11101101$에 대하여 수정해서 구현해 봅시다. 결과가 예상대로입니까? 설명해 봅시다."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 5. 참고문헌<a id=\"references\"></a>\n",
+        "\n",
+        "1. Ethan Bernstein and Umesh Vazirani (1997) \"Quantum Complexity Theory\" SIAM Journal on Computing, Vol. 26, No. 5: 1411-1473, [doi:10.1137/S0097539796300921](https://doi.org/10.1137/S0097539796300921).\n",
+        "2. Jiangfeng Du, Mingjun Shi, Jihui Wu, Xianyi Zhou, Yangmei Fan, BangJiao Ye, Rongdian Han (2001) \"Implementation of a quantum algorithm to solve the Bernstein-Vazirani parity problem without entanglement on an ensemble quantum computer\", Phys. Rev. A 64, 042306, [10.1103/PhysRevA.64.042306](https://doi.org/10.1103/PhysRevA.64.042306), [arXiv:quant-ph/0012114](https://arxiv.org/abs/quant-ph/0012114). "
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 10,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "name": "stderr",
+          "output_type": "stream",
+          "text": [
+            "/usr/local/anaconda3/envs/terra-unstable/lib/python3.9/site-packages/qiskit/aqua/__init__.py:86: DeprecationWarning: The package qiskit.aqua is deprecated. It was moved/refactored to qiskit-terra For more information see <https://github.com/Qiskit/qiskit-aqua/blob/main/README.md#migration-guide>\n",
+            "  warn_package('aqua', 'qiskit-terra')\n"
+          ]
+        },
+        {
+          "data": {
+            "text/html": [
+              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.19.0</td></tr><tr><td><code>qiskit-aer</code></td><td>0.9.1</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.6.0</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.17.0</td></tr><tr><td><code>qiskit-aqua</code></td><td>0.9.5</td></tr><tr><td><code>qiskit</code></td><td>0.31.0</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.9.7</td></tr><tr><td>Python compiler</td><td>Clang 10.0.0 </td></tr><tr><td>Python build</td><td>default, Sep 16 2021 08:50:36</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>32.0</td></tr><tr><td colspan='2'>Fri Nov 05 14:14:51 2021 GMT</td></tr></table>"
+            ],
+            "text/plain": [
+              "<IPython.core.display.HTML object>"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "import qiskit.tools.jupyter\n",
+        "%qiskit_version_table"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 2
+}

From 1721a5ceab68736ef1e6fb8b5786e60b5e7341e2 Mon Sep 17 00:00:00 2001
From: mt-gitlocalize <mt@gitlocalize.com>
Date: Thu, 9 Jun 2022 11:39:17 +0000
Subject: [PATCH 25/62] Translate bernstein-vazirani.ipynb via GitLocalize

---
 .../ko/ch-algorithms/bernstein-vazirani.ipynb  | 18 +++++++++---------
 1 file changed, 9 insertions(+), 9 deletions(-)

diff --git a/translations/ko/ch-algorithms/bernstein-vazirani.ipynb b/translations/ko/ch-algorithms/bernstein-vazirani.ipynb
index 1462fb17e..76ad38edc 100644
--- a/translations/ko/ch-algorithms/bernstein-vazirani.ipynb
+++ b/translations/ko/ch-algorithms/bernstein-vazirani.ipynb
@@ -40,7 +40,7 @@
         "\n",
         "일반적으로 오라클은 $$f_s(x) = s \\cdot x \\mod 2$$를 입력하면 $x$를 반환합니다. 따라서 숨겨진 비트 문자열 $s$는 여러가지 입력값들로 오라클을 탐색하여 드러낼 수 있습니다.\n",
         "\n",
-        "Input(x)\n",
+        "입력(x)\n",
         ":-:\n",
         "100...0\n",
         "010...0\n",
@@ -77,7 +77,7 @@
         "\n",
         " 우리는 Hadamard가 하나의 큐비트에서 다음 변환을 수행한다는 것을 기억합니다.\n",
         "\n",
-        "$$ H|0\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) $$ $$ H|1\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle) $$\n",
+        "$$ H|0\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) $$ $$ H|1\\rangle = \\tfrac{1}{\\sqrt{ 2}}(|0\\rangle - |1\\rangle) $$\n",
         "\n",
         "합 표기을 사용하여 다음과 같이 다시 작성할 수 있습니다.\n",
         "\n",
@@ -85,11 +85,11 @@
         "\n",
         "두 개의 큐비트에 대해 각각에 Hadamard를 적용하면 다음 변환이 수행됩니다.\n",
         "\n",
-        "$$ H^{\\otimes 2}|00\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle) $$ $$ H^{\\otimes 2}|01\\rangle = \\tfrac{1}{2}(|00\\rangle - |01\\rangle + |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}|10\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle - |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}|11\\rangle = \\tfrac{1}{2}(|00\\rangle - |01\\rangle - |10\\rangle + |11\\rangle) $$\n",
+        "$$ H^{\\otimes 2}|00\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle) $$ $$ H^{ \\otimes 2}|01\\rangle = \\tfrac{1}{2}(|00\\rangle - |01\\rangle + |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}| 10\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle - |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}|11\\rangle = \\ tfrac{1}{2}(|00\\rangle - |01\\rangle - |10\\rangle + |11\\rangle) $$\n",
         "\n",
         "합을 사용하여 아래와 같이 표현할 수 있습니다.\n",
         "\n",
-        "$$ H^{\\otimes 2}|a\\rangle = \\frac{1}{2}\\sum_{x\\in {0,1}^2} (-1)^{a\\cdot x}|x\\rangle $$\n",
+        "$$ H^{\\otimes 2}|a\\rangle = \\frac{1}{2}\\sum_{x\\in {0,1}^2} (-1)^{a\\cdot x}|x\\ 범위 $$\n",
         "\n",
         "이제 위의 수식을 도출해 보도록 합시다.\n",
         "\n",
@@ -98,7 +98,7 @@
         "\n",
         "특히, 양자 레지스터 $|00\\dots 0\\rangle$ 상태로 시작하여 $n$ Hadamard 게이트를 적용하면 익숙한 양자 중첩 상태를 얻게 됩니다.\n",
         "\n",
-        "$$ |00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} |x\\rangle $$\n",
+        "$$ |00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} |x \\rangle $$\n",
         "\n",
         "이 경우 $a=0$이므로 위상 항 $(-1)^{a\\cdot x}$는 사라집니다. 따라서 $(-1)^{a\\cdot x} = 1$입니다.\n",
         "\n",
@@ -108,11 +108,11 @@
         "\n",
         "숨겨진 비트 문자열을 드러내는 알고리즘은 $|00\\dots 0\\rangle$의 Hadamard 변환에서 얻은 양자 중첩으로 양자 오라클 $f_s$를 쿼리하여 얻어집니다. 즉,\n",
         "\n",
-        "$$ |00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} |x\\rangle \\xrightarrow{f_a} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^{a\\cdot x}|x\\rangle $$\n",
+        "$$ |00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} |x \\rangle \\xrightarrow{f_a} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^{a\\cdot x}|x\\rangle $$\n",
         "\n",
         "$n$ Hadamard 게이트의 역수는 다시 $n$ Hadamard 게이트이므로 $a$를 얻을 수 있습니다.\n",
         "\n",
-        "$$ \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^{a\\cdot x}|x\\rangle \\xrightarrow{H^{\\otimes n}} |a\\rangle $$"
+        "$$ \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^{a\\cdot x}|x\\rangle \\xrightarrow{H^ {\\otimes n}} |a\\rangle $$"
       ]
     },
     {
@@ -144,9 +144,9 @@
         "   <li>$s=11$ 문자열에 대해 양자 오라클은 $$ |x \\rangle \\xrightarrow{f_s} (-1)^{x\\cdot 11} |x \\rangle$$ 연산을 수행합니다.</li>\n",
         "\n",
         "\n",
-        "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( (-1)^{00\\cdot 11}|00\\rangle + (-1)^{01\\cdot 11}|01\\rangle + (-1)^{10\\cdot 11}|10\\rangle + (-1)^{11\\cdot 11}|11\\rangle \\right)$$\n",
+        "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( (-1)^{00\\cdot 11}|00\\rangle + (-1)^{01\\cdot 11}|01\\ rangle + (-1)^{10\\cdot 11}|10\\rangle + (-1)^{11\\cdot 11}|11\\rangle \\right)$$\n",
         "\n",
-        "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle - \\lvert 0 1 \\rangle - \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)$$\n",
+        "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle - \\lvert 0 1 \\rangle - \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right) $$\n",
         "\n",
         "   \n",
         "\n",

From 1e8f0db0fe829307193077acca2174ed30c752eb Mon Sep 17 00:00:00 2001
From: mt-gitlocalize <mt@gitlocalize.com>
Date: Thu, 9 Jun 2022 11:41:58 +0000
Subject: [PATCH 26/62] Translate introduction.ipynb via GitLocalize

---
 translations/ko/ch-states/introduction.ipynb | 110 +++++++++++++++++++
 1 file changed, 110 insertions(+)
 create mode 100644 translations/ko/ch-states/introduction.ipynb

diff --git a/translations/ko/ch-states/introduction.ipynb b/translations/ko/ch-states/introduction.ipynb
new file mode 100644
index 000000000..8e5c45500
--- /dev/null
+++ b/translations/ko/ch-states/introduction.ipynb
@@ -0,0 +1,110 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "tags": [
+          "remove_cell"
+        ]
+      },
+      "source": [
+        "# 소개\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_aKbLuy0bVc"
+      },
+      "source": [
+        "If you think quantum mechanics sounds challenging, you are not alone. All of our intuitions are based on day-to-day experiences, and so are better at understanding the behavior of balls and bananas than atoms or electrons. Though quantum objects can seem random and chaotic at first, they just follow a different set of rules. Once we know what those rules are, we can use them to create new and powerful technology. Quantum computing will be the most revolutionary example of this."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "![이미지1](images/atoms10.png)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "goals": [
+          {
+            "id": "bitdescription"
+          }
+        ]
+      },
+      "source": [
+        "양자 컴퓨팅을 향한 여정을 시작하기 위해 이미 알고 있는 것을 테스트해 보겠습니다.\n",
+        "\n",
+        "### Quick Exercise\n",
+        "\n",
+        "다음 중 *비트* 에 대한 설명으로 옳은 것은?\n",
+        "\n",
+        "- The smallest unit of information: either a `0` or a `1`.\n",
+        "- A blade used by a carpenter.\n",
+        "- Something you put in a horse's mouth."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "gloss": {
+          "qubit": {
+            "text": "A __qubit__ or __quantum bit__ is the basic unit of quantum information. It is a two-state quantum-mechanical system, and one of the simplest systems displaying the peculiarity of quantum mechanics.",
+            "title": "Qubit"
+          }
+        },
+        "id": "gl_lYB00no22n"
+      },
+      "source": [
+        "Actually, they are all correct: it's a very multi-purpose word! But if you chose \"the smallest unit of information\", it shows that you are already thinking along the right lines. The idea that information can be stored and processed as a series of ```0```s and ```1```s is quite a big conceptual hurdle, but it's something most people today know without even thinking about it. Taking this as a starting point, we can start to imagine bits that obey the rules of quantum mechanics. These [quantum bits](gloss:qubit), or *qubits*, will then allow us to process information in new and different ways.\n",
+        "\n",
+        "We'll start diving deeper into the world of qubits. For this, we'll need some way of keeping track of what they are doing when we apply gates. The most powerful way to do this is to use the mathematical language of vectors and matrices.\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "![이미지2](images/bloch.png)\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_NUxGaBUrp3"
+      },
+      "source": [
+        "This chapter will be most effective for readers who are already familiar with vectors and matrices. Those who aren't familiar will likely be fine too, though it might be useful to consult our [Introduction to Linear Algebra for Quantum Computing](/course/ch-appendix/an-introduction-to-linear-algebra-for-quantum-computing) from time to time.\n",
+        "\n",
+        "Since we will be using Qiskit, our Python-based framework for quantum computing, it would also be useful to know the basics of Python. Those who need a primer can consult the [Introduction to Python and Jupyter notebooks](/course/ch-prerequisites/introduction-to-python-and-jupyter-notebooks)."
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 2
+}

From 1033f8268d793d5cfe6b0d6fb97cf6e7c7ffb985 Mon Sep 17 00:00:00 2001
From: glucktak <glucktak@gmail.com>
Date: Thu, 9 Jun 2022 11:41:59 +0000
Subject: [PATCH 27/62] Translate introduction.ipynb via GitLocalize

---
 translations/ko/ch-states/introduction.ipynb | 23 +++++++++-----------
 1 file changed, 10 insertions(+), 13 deletions(-)

diff --git a/translations/ko/ch-states/introduction.ipynb b/translations/ko/ch-states/introduction.ipynb
index 8e5c45500..aaaab4a1a 100644
--- a/translations/ko/ch-states/introduction.ipynb
+++ b/translations/ko/ch-states/introduction.ipynb
@@ -14,10 +14,9 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_aKbLuy0bVc"
       },
       "source": [
-        "If you think quantum mechanics sounds challenging, you are not alone. All of our intuitions are based on day-to-day experiences, and so are better at understanding the behavior of balls and bananas than atoms or electrons. Though quantum objects can seem random and chaotic at first, they just follow a different set of rules. Once we know what those rules are, we can use them to create new and powerful technology. Quantum computing will be the most revolutionary example of this."
+        "양자 역학이 어렵다고 생각한다면, 여러분은 혼자가 아닙니다. 우리의 모든 직관은 일상적인 경험을 기반으로 하기 때문에 우리에게는 원자나 전자보다 공의 움직임이나 바나나가 더 이해하기 쉽습니다. 양자 물체의 행동은 무작위적이고 혼란스러워 보이겠지만, 단지 다른 규칙을 따르는 것일 뿐입니다. 이러한 규칙이 무엇인지 알게 되면 이를 사용하여 새롭고 강력한 기술을 만들 수 있습니다. 양자 컴퓨팅은 그 기술의 가장 혁신적인 예가 될 것입니다."
       ]
     },
     {
@@ -40,13 +39,13 @@
       "source": [
         "양자 컴퓨팅을 향한 여정을 시작하기 위해 이미 알고 있는 것을 테스트해 보겠습니다.\n",
         "\n",
-        "### Quick Exercise\n",
+        "### 간단한 연습\n",
         "\n",
         "다음 중 *비트* 에 대한 설명으로 옳은 것은?\n",
         "\n",
-        "- The smallest unit of information: either a `0` or a `1`.\n",
-        "- A blade used by a carpenter.\n",
-        "- Something you put in a horse's mouth."
+        "- 정보의 가장 작은 단위: `0` 또는 `1`\n",
+        "- 목수가 사용하는 대패의 날\n",
+        "- 말의 입에 물리는 재갈"
       ]
     },
     {
@@ -57,13 +56,12 @@
             "text": "A __qubit__ or __quantum bit__ is the basic unit of quantum information. It is a two-state quantum-mechanical system, and one of the simplest systems displaying the peculiarity of quantum mechanics.",
             "title": "Qubit"
           }
-        },
-        "id": "gl_lYB00no22n"
+        }
       },
       "source": [
-        "Actually, they are all correct: it's a very multi-purpose word! But if you chose \"the smallest unit of information\", it shows that you are already thinking along the right lines. The idea that information can be stored and processed as a series of ```0```s and ```1```s is quite a big conceptual hurdle, but it's something most people today know without even thinking about it. Taking this as a starting point, we can start to imagine bits that obey the rules of quantum mechanics. These [quantum bits](gloss:qubit), or *qubits*, will then allow us to process information in new and different ways.\n",
+        "사실, 모두 정답입니다. 비트라는 발음의 여러가지 단어와 뜻이 있습니다. 하지만, 여러분이 \"정보의 최소 단위\"를 선택했다면 이미 이 강의가 의도하는 방향으로 생각하고 있는 겁니다. 정보가 일련의 `0` 과 `1` 로 저장되고 처리된다는 것은 상당히 큰 개념적 장애물이지만 오늘날 대부분의 사람들은 생각할 필요도 없이 알고 있는 것입니다. 이 개념에서 출발해서 양자 역학의 규칙을 따르는 비트를 상상할 수 있습니다. 이러한 [양자 비트](gloss:qubit) 또는 *큐비트* 를 사용하면 새롭고 다양한 방식으로 정보를 처리할 수 있습니다.\n",
         "\n",
-        "We'll start diving deeper into the world of qubits. For this, we'll need some way of keeping track of what they are doing when we apply gates. The most powerful way to do this is to use the mathematical language of vectors and matrices.\n"
+        "이제 우리는 큐비트의 세계 속으로 더 깊이 파고들 것입니다. 그러기 위해서는 게이트를 적용할 때 그들이 무엇을 하고 있는지 추적할 수 있는 방법이 필요합니다. 이를 수행하는 가장 강력한 방법은 벡터와 행렬의 수학적 언어를 사용하는 것입니다.\n"
       ]
     },
     {
@@ -77,12 +75,11 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_NUxGaBUrp3"
       },
       "source": [
-        "This chapter will be most effective for readers who are already familiar with vectors and matrices. Those who aren't familiar will likely be fine too, though it might be useful to consult our [Introduction to Linear Algebra for Quantum Computing](/course/ch-appendix/an-introduction-to-linear-algebra-for-quantum-computing) from time to time.\n",
+        "이 장은 이미 벡터와 행렬에 익숙한 독자들을 위해서 가장 효과적이지만, 익숙하지 않은 사람들도 괜찮습니다. 하지만, 가끔 [양자 컴퓨팅을 위한 선형 대수 소개를](https://qiskit.org/textbook/ch-appendix/linear_algebra.html) 참조하는 것이 도움이 될 것입니다.\n",
         "\n",
-        "Since we will be using Qiskit, our Python-based framework for quantum computing, it would also be useful to know the basics of Python. Those who need a primer can consult the [Introduction to Python and Jupyter notebooks](/course/ch-prerequisites/introduction-to-python-and-jupyter-notebooks)."
+        "양자 컴퓨팅을 위한 Python 기반 프레임워크인 Qiskit을 사용할 것이기 때문에 Python의 기본 사항을 아는 것도 유용할 것입니다. 입문서가 필요한 사람들은 [Python 및 Jupyter 노트북 소개를](https://qiskit.org/textbook/ch-prerequisites/python-and-jupyter-notebooks.html) 참조하십시오."
       ]
     }
   ],

From 987729309ec05b52b331e035c7bcf6af0756d729 Mon Sep 17 00:00:00 2001
From: //va <vabarbosa@users.noreply.github.com>
Date: Thu, 9 Jun 2022 09:34:35 -0400
Subject: [PATCH 28/62] feat: update links to new learn page (#1058)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

* Update utilities.ts

* update test

* Changed url in the README

Co-authored-by: Randy <randytolentino@ibm.com>
Co-authored-by: David <9059044+Tansito@users.noreply.github.com>
Co-authored-by: Eddybrando Vásquez <eddybrando.vasquez@gmail.com>
---
 README.md                           | 2 +-
 cypress/integration/sidebar.spec.js | 2 +-
 server/utilities.ts                 | 2 +-
 3 files changed, 3 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index b995ebc59..454d3bf3e 100644
--- a/README.md
+++ b/README.md
@@ -1,5 +1,5 @@
 # platypus
-This repository is home of the new [Qiskit Textbook (beta)](https://qiskit.org/textbook-beta/).
+This repository is home of the new [Qiskit Textbook (beta)](https://qiskit.org/learn/).
 
 The previous version of the Qiskit Textbook textbook can be found [here](https://github.com/qiskit-community/qiskit-textbook).
 
diff --git a/cypress/integration/sidebar.spec.js b/cypress/integration/sidebar.spec.js
index 59d4da8e0..022f4aee1 100644
--- a/cypress/integration/sidebar.spec.js
+++ b/cypress/integration/sidebar.spec.js
@@ -39,7 +39,7 @@ describe('Sidebar', () => {
   it('back to home link links to textbook home', () => {
     const viewports = ['ipad-2', 'macbook-15']
     const linkSelector = '[data-test=back-to-home-link]'
-    const textbookHomeUrl = 'https://qiskit.org/textbook-beta'
+    const textbookHomeUrl = 'https://qiskit.org/learn'
 
     viewports.forEach((viewport) => {
       cy.viewport(viewport)
diff --git a/server/utilities.ts b/server/utilities.ts
index fb335347e..5c8f257ba 100644
--- a/server/utilities.ts
+++ b/server/utilities.ts
@@ -23,7 +23,7 @@ import {
 
 import { IS_PRODUCTION } from './configuration'
 
-const TEXTBOOK_HOME = 'https://qiskit.org/textbook-beta'
+const TEXTBOOK_HOME = 'https://qiskit.org/learn'
 
 const DEFAULT_SHARED_FOLDER = path.join(CONTENT_DIR, 'shared')
 

From 40c159796f708f7bdce35908d8ee2438a55f2161 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Thu, 9 Jun 2022 17:56:34 +0200
Subject: [PATCH 29/62] updated packages files

---
 package-lock.json | 28947 +-------------------------------------------
 package.json      |     2 +-
 2 files changed, 209 insertions(+), 28740 deletions(-)

diff --git a/package-lock.json b/package-lock.json
index 6e36efe25..78170e823 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -1,28524 +1,8 @@
 {
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+      "integrity": "sha512-KMvVuFzpKBuiIXW3E4u3mySRO2/mCHSyZDJQM5NQ9Q9KHWHWh0NHgfbRMLLrceUK5qAL4ytALJbpRMjixFZh8A=="
     },
     "xdg-basedir": {
       "version": "4.0.0",
@@ -50903,8 +22373,7 @@
     "xtend": {
       "version": "4.0.2",
       "resolved": "https://registry.npmjs.org/xtend/-/xtend-4.0.2.tgz",
-      "integrity": "sha512-LKYU1iAXJXUgAXn9URjiu+MWhyUXHsvfp7mcuYm9dSUKK0/CjtrUwFAxD82/mCWbtLsGjFIad0wIsod4zrTAEQ==",
-      "devOptional": true
+      "integrity": "sha512-LKYU1iAXJXUgAXn9URjiu+MWhyUXHsvfp7mcuYm9dSUKK0/CjtrUwFAxD82/mCWbtLsGjFIad0wIsod4zrTAEQ=="
     },
     "y-codemirror": {
       "version": "3.0.1",
diff --git a/package.json b/package.json
index 7a242824a..460d9dc9b 100644
--- a/package.json
+++ b/package.json
@@ -77,7 +77,7 @@
     "lit-element": "^2.5.1",
     "lodash": "^4.17.21",
     "markdown-it": "^12.2.0",
-    "mathjax-full": "^3.2.1",
+    "mathjax-full": "^3.2.2",
     "mathjs": "^10.6.1",
     "mongodb": "4.3.1",
     "nanoid": "^3.3.4",

From 2bd866be5d000cefa943e8b0bebf72994f6f412a Mon Sep 17 00:00:00 2001
From: Yunzhe <dran.z@foxmail.com>
Date: Thu, 9 Jun 2022 17:26:57 +0000
Subject: [PATCH 30/62] Translate why-quantum-computing.ipynb via GitLocalize

---
 .../zh-CN/intro/why-quantum-computing.ipynb   | 324 ++++++++++++++++++
 1 file changed, 324 insertions(+)
 create mode 100644 translations/zh-CN/intro/why-quantum-computing.ipynb

diff --git a/translations/zh-CN/intro/why-quantum-computing.ipynb b/translations/zh-CN/intro/why-quantum-computing.ipynb
new file mode 100644
index 000000000..55b3c5ea1
--- /dev/null
+++ b/translations/zh-CN/intro/why-quantum-computing.ipynb
@@ -0,0 +1,324 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "# 我们为什么需要量子计算？"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 什么是计算机？\n",
+        "\n",
+        "既然你已经成功访问了这个网页，你应该已经知道什么是计算机了吧。今天的计算机有许多种形式：从笔记本电脑或智能手机到控制交通信号灯的系统，计算机似乎可以做任何事情！这些系统可能非常复杂和专业，但它们都有一个共同点：计算机根据一些输入信息执行一组指令，来为我们提供一些新的（输出）信息。\n",
+        "\n",
+        "我们给计算机的指令需要非常具体和明确。我们称这些指令为*算法，*并且许多关于计算机的研究都是针对不同算法的行为。在本课程中，我们将只考虑最简单的计算机：没有键盘、鼠标或屏幕——只有信息和算法。\n",
+        "\n",
+        "![An artists rendering of basically all computers](images/why-qc/basically_all_computers.png)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "formulas": {
+          "T": {
+            "meaning": "This is the average time our search algorithm takes to run.",
+            "type": "Locally defined variable"
+          },
+          "exp": {
+            "meaning": "This is the number of digits in our secret number. Because this is a superscript, this means we are doing 10 to the power of d.",
+            "type": "Locally defined variable"
+          },
+          "prop_to": {
+            "meaning": "'Proportional to': Everything to the left of this symbol is <a href='https://en.wikipedia.org/wiki/Proportionality_(mathematics)'>proportional to</a> the things on the right.",
+            "type": "Universal notation"
+          }
+        },
+        "gloss": {
+          "resources": {
+            "text": "A resource is anything the algorithm needs to run. In computer science, this usually means either the time needed by the algorithm, or the space (e.g. computer memory).",
+            "title": "Resources"
+          }
+        }
+      },
+      "source": [
+        "## 对计算机算法归类\n",
+        "\n",
+        "要了解量子计算机在现代传统计算机中的作用，我们首先需要了解如何衡量不同算法的性能。\n",
+        "\n",
+        "在计算机科学中，我们根据算法使用的[资源](gloss:resources)如何随着输入的大小而增长对算法进行分类。我们称之为算法的*复杂度*（包括时间复杂度与空间复杂度，我们以下讨论的均为时间复杂度）。例如，确定一个数字是否为偶数的算法只需要检查该数字中的最后一位数字。在这种情况下，“输入”是一个数字，输出是“偶数”或“奇数”。我们将这种算法称其为*恒定时间*算法，因为算法完成所需的时间不取决于输入数字的大小。不同的计算机可能需要不同的时间才能得到这个结果，但这是由于其他因素而不是输入的长度。\n",
+        "\n",
+        "![The steps of an algorithm that works out if a number is even or odd](images/why-qc/odd-even-algo.svg)\n",
+        "\n",
+        "让我们再看一个不同的例子。这一次，输入的是两个等长的数，而问题是把它们加在一起。在这种情况下，输出将是一个新数字。当对两个多位数进行求和时，你在学校大概率学到的一种常见算法是从每个数字中最右边的数字开始，然后将它们加在一起。然后我们向左移动一位数（如果结果大于 9，则进位“1”）并重复该过程。计算机重复此操作直到没有更多数字要添加，算法即结束。\n",
+        "\n",
+        "![Animation showing the steps of an addition algorithm](images/why-qc/adding-algo.svg)\n",
+        "\n",
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### 加法的复杂度是怎样的？\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"intro-why-qc-0\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\n",
+        "此加法算法完成所需的时间...\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option(correct) -->\n",
+        "\n",
+        "1. ...随着输入数字的长度线性（成比例地）增长（线性时间）。\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. ...不受输入数字长度的影响（恒定时间）。\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. ...随着输入数字长度的平方增长（二次时间）。\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "同样，不同的计算机将以不同的速度执行该算法；笔记本电脑可以比人类快数百万倍地执行加法。但是，无论你可以在一秒钟内进行一百万次操作还是只能一次操作，其增长率都是一样的。\n",
+        "\n",
+        "![graph of constant and linear running times vs input sizes for different running times](images/why-qc/graph-linear-constant.svg)\n",
+        "\n",
+        "最后有一个对我们来说非常特别有趣的例子。假设我有一个秘密号码（例如 PIN），问题是猜对它。在这种情况下，问题的大小是数字的长度。\n",
+        "\n",
+        "让我们假设检查答案是否正确的唯一方法是将其输入数字键盘。由于我们没有关于这个号码的信息，寻找这个秘密号码的最佳算法是使用“穷举”方法：这意味着算法没有做任何聪明的事情，只是简单地尝试每个可能的数字。\n",
+        "\n",
+        "这需要多长时间？现在，理论上我们可以幸运地一口气猜出答案，但这不太可能。平均而言，我们必须尝试大约一半的可能输入，因此我们算法的运行时间与可能组合的数量成正比。现在的问题变成了：可能组合的数量如何随着秘密号码的长度而增长？\n",
+        "\n",
+        "![Animation showing the steps of a brute-force search algorithm](images/why-qc/search-algo.svg)\n",
+        "\n",
+        "我们在密码中每添加一个位数都会使可能的情况增加到原来的 10 倍。例如，具有 1 位数字的密码有 10 个可能的值（0、1、2、3、4、5、6、7、8 和 9），一个 2 位的密码有 100 个可能的值。假设猜测每个数字所花费的时间相同（无论长度如何），我们可以这样在数学上表示：\n",
+        "\n",
+        "$$ \\cssId{T}{T} \\cssId{prop_to}{\\propto} 10^\\cssId{exp}{d}$$\n",
+        "\n",
+        "你会注意到位数（d）是该等式中的指数，因此我们说这是一个*指数时间*算法，即运行时间随着输入的长度呈指数增长。\n",
+        "\n",
+        "![graph of constant, linear and exponential running times vs input sizes for different running times](images/why-qc/graph-all.svg)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "gloss": {
+          "intractable": {
+            "text": "An intractable problem is one which can be solved in theory, but requires too many resources in practice.",
+            "title": "Intractable"
+          }
+        }
+      },
+      "source": [
+        "## 我们为什么这样度量算法？\n",
+        "\n",
+        "不同的电脑有不同的长处；在一台计算机上的某些操作可能比另一台计算机更快。通过研究算法运行时间与输入大小的增长关系，我们可以忽略特定设备的细节并实际度量*算法*，而不是算法和计算机的特定组合。更重要的是，了解算法如何随输入大小扩展也可以告诉我们该算法是否会在可控范围内增长。\n",
+        "\n",
+        "让我们考虑一下我们在上面看到的线性时间加法算法。如果我们可以在一秒钟内对两个 10 位数字求和，由于线性增长率，我们应该能够在两秒钟内对两个 20 位数字求和。每多出 10 位数字，我们的计算时间就会增加大约一秒。\n",
+        "\n",
+        "相比之下，假设你可以使用上面的指数时间搜索算法在 1 秒内找到一个 10 位数的 PIN。这意味着你的计算机速度足以每秒尝试约 5,000,000,000 次组合。我们预计同样的计算机大约需要 5,000,000,000 秒（约 150 年）才能找到 20 位数的 PIN。再增加 10 位数字会将其增加到大约 150,000,000,000 年（大约是宇宙年龄的 120 倍）。即使是中等大小的输入（在这个例子中约为30位数字），指数时间算法甚至都不能说很困难，而是根本无法执行。\n",
+        "\n",
+        "虽然为了尽量简单地讲清楚问题，我们人为构造了一个 PIN 查找的例子，但计算机科学中有许多实际问题，对于这些问题我们目前只有低效的算法。尽管今天计算机的速度是非常震撼的，但即使是最大的超级计算机，这些[棘手](gloss:intractable)的问题也可能太难了。\n",
+        "\n",
+        "但是，如果我们能找到更高效的算法，哪怕使用相对较慢或不可靠的计算机，这些棘手的问题可能会突然变得在我们掌控能力范围内。这就是量子计算的用武之地。\n",
+        "\n",
+        "## 量子计算如何帮助我们？\n",
+        "\n",
+        "到目前为止，我们都在以一种非常抽象的方式来考虑算法，但是执行这些算法的计算机必须存在于现实世界中。无论这些计算机是高性能的微芯片，还是带有纸笔的人类，所有的计算机最终都受物理定律的支配。它们可以执行的操作限制了我们可以创建的算法。\n",
+        "\n",
+        "物理学试图找出宇宙中所有事物都遵循的一套规则。大约在 20 世纪初，通过实验室的精密实验，物理学家看到了他们当时的物理学无法解释的奇怪现象。这意味着原有的规则不太准确，因此他们开发了更完整的“量子”物理学以更好地描述这类现象。\n",
+        "\n",
+        "物理学家创造了量子物理学来解释他们以前从未见过的现象，而计算机科学家发现他们可以（理论上）利用这种新发现的现象来创建更高效的算法。因此，一些我们认为对于传统计算机来说棘手的问题，对于利用这类新现象的“量子”计算机而言是在掌控范围内的。其中一个问题是*因数分解*。\n",
+        "\n",
+        "假设我们有一个整数 '$x$'。因数分解算法的目标是找到整数 $p$ 和 $q$ 使得 $p×q = x$。有时这很简单：例如你一眼就能看出 $2000 = 2 × 1000$。但是如果 $x$ 是两个大素数的乘积，这个问题就变得非常困难了。当我们谈论因数分解时，我们将假设最困难（最坏情况）的情景。在下面的代码单元格中，我们为变量 <code>x</code> 指定了一个 250 位数字："
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 1,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "x = 2140324650240744961264423072839333563008614715144755017797754920881418023447140136643345519095804679610992851872470914587687396261921557363047454770520805119056493106687691590019759405693457452230589325976697471681738069364894699871578494975937497937"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "gloss": {
+          "coreyears": {
+            "text": "Conventional computer chips are often made from processors called <a href=\"https://en.wikipedia.org/wiki/Multi-core_processor\">\"cores\"</a>. A <i>core-year</i> is the equivalent of using one of these cores continuously for a year. For reference, a modern laptops have around 2-4 cores. The meaning of this number depends on how powerful the core is, but this should give you a rough idea of the computing power involved.",
+            "title": "Core Year"
+          }
+        }
+      },
+      "source": [
+        "2020 年，研究人员使用经典的超级计算机并花费了约 2700 [核年](gloss:coreyears)的算力对这个数字进行了因数分解。这是一项巨大的努力，并且至今依然保持世界纪录。我们可以在下面的代码单元中验证他们的结果（万幸，乘法算法是高效的！）："
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 2,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "text/plain": [
+              "True"
+            ]
+          },
+          "execution_count": 2,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "p = 64135289477071580278790190170577389084825014742943447208116859632024532344630238623598752668347708737661925585694639798853367\n",
+        "q = 33372027594978156556226010605355114227940760344767554666784520987023841729210037080257448673296881877565718986258036932062711\n",
+        "\n",
+        "p*q == x  # Evaluates to 'True'"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "gloss": {
+          "RSA": {
+            "text": "RSA numbers are numbers taken from the RSA factoring challenge. These numbers are intentionally chosen to be difficult to factor.<p>'RSA' are the initials of three of the people that invented the protocol that uses these large numbers to encrypt information.",
+            "title": "RSA Number"
+          }
+        }
+      },
+      "source": [
+        "显示的输出是代码单元最后一行的值。在这种情况下，我们可以看到 <code>p*q == x</code> 的计算结果为 <code>True</code>。虽然没有经过数学证明，但我们很确定传统计算机没有高效的算法来分解这些数字。事实上，互联网的大部分加密原理都依赖这样一个假设：因数分解问题是棘手的，因而经典计算机不可能分解 617 位的 [RSA](gloss:RSA) 数字。相比之下，我们知道量子计算机的高效因数分解算法。一旦我们拥有足够大的量子计算机，我们估计可以在一天内分解这些数字。"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "gloss": {
+          "noise": {
+            "text": "Noise is useless information that's difficult to distinguish from useful information. For example, it's hard to hear someone talking to you if there are lots of other people talking loudly nearby.",
+            "title": "Noise"
+          },
+          "qiskit": {
+            "text": "Qiskit is a software development kit for working with quantum computers.",
+            "title": "Qiskit"
+          },
+          "qubits": {
+            "text": "A 'qubit' is a 'quantum bit'. We will study these later in this course.",
+            "title": "Qubit"
+          },
+          "transistor": {
+            "text": "A transistor is an electronic device. They can be used to switch electric currents on and off, and can be used to build a computer processor.",
+            "title": "Transistor"
+          }
+        }
+      },
+      "source": [
+        "## 我们现在处于什么阶段？\n",
+        "\n",
+        "现在我们知道量子计算机可以执行更高效的算法。但我们目前拥有的量子计算机体量太小且不够稳定，无法提供相对传统计算机的计算优势。\n",
+        "\n",
+        "在一个非常简单的层面上，有两个因素限制了我们的量子计算机可以解决的问题的大小。首先是他们可以存储和处理的数据量，这个我们通常以 [*量子比特*](gloss:qubits) 来衡量。如果我们没有足够的量子比特，我们根本无法存储和处理超过一定规模的问题。第二个是量子计算机的错误率。由于我们只能在精密的实验室实验中看到量子行为，制造量子计算机也是一个复杂的过程。我们现在拥有的量子计算机还很嘈杂，这意味着它经常会出错并在最终结果中引入“[噪声](gloss:noise)”。如果噪声太大，我们从中得到结果将没有任何意义！\n",
+        "\n",
+        "目前，我们拥有的量子计算机是实验性的。量子计算机受到量子比特数和错误率的限制，因此其目前可以解决的问题对于传统计算机来说依然可以轻松解决。\n",
+        "\n",
+        "但在未来的某个时候，这种情况或许将会改变。我们将达到“量子优势”，这意味着使用量子计算机解决问题比传统计算机更具有实际经济意义。为什么我们有这样的自信？*因为我们通过算法的增长率来度量算法！*我们知道，只要量子计算机继续稳步发展，其最终会取代经典计算机。\n",
+        "\n",
+        "![comparison of (projected) classical vs quantum factoring abilities over time](images/why-qc/q-vs-c.svg)\n",
+        "\n",
+        "如果想在一天内分解一个 617 位 RSA 数字，我们估计需要大约 2000 万个有噪声的量子比特。在撰写本文时，IBM 目前拥有一台 65 量子比特的量子计算机，并计划到 2023 年之前创造一个拥有超过 1000 个量子比特的系统。我们相信还有许多其他算法将在这个里程碑到来之前为我们带来量子优势，但我们依然还有很长的路要走。\n",
+        "\n",
+        "我们应该提醒一下自己传统计算机的来历。下图是世界上第一个[晶体管](gloss:transistor)，创造于 1947 年。晶体管是现代计算机处理器的组成部分。\n",
+        "\n",
+        "![comparison of (projected) classical vs quantum factoring abilities over time](images/why-qc/first-transistor.jpg) Image credit: Federal employee <a href=\"https://clintonwhitehouse4.archives.gov/Initiatives/Millennium/capsule/mayo.html\">Link</a>, <a href=\"https://commons.wikimedia.org/w/index.php?curid=554340\">Public Domain</a>.\n",
+        "\n",
+        "70 年后的今天，我们的现代计算机芯片可以包含数十亿个晶体管。\n",
+        "\n",
+        "在本课程剩下的部分，我们将探索能帮助我们创建更高效算法的量子效应。在本课程结束时，你将能够使用软件库 [Qiskit](gloss:qiskit) 对量子计算机进行编程以运行其中一种算法。"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### 课后小测\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"intro-why-qc-1\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\n",
+        "量子计算机最终将...\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option(correct) -->\n",
+        "\n",
+        "1. ...计算对传统计算机来说太难的问题。\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. ...替代传统计算机。\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. ...提高传统计算机的速度。\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 4
+}

From 1373d34f4e80146d8fa3d8d74d56de9d0ed65cca Mon Sep 17 00:00:00 2001
From: techtolentino <makertolentino@gmail.com>
Date: Thu, 9 Jun 2022 12:05:56 -0700
Subject: [PATCH 31/62] remove unnecessary comment

---
 .../UserAccount/ClassroomSection.vue          | 75 +++++++++++--------
 1 file changed, 43 insertions(+), 32 deletions(-)

diff --git a/frontend/vue/components/UserAccount/ClassroomSection.vue b/frontend/vue/components/UserAccount/ClassroomSection.vue
index cde034291..5319b812c 100644
--- a/frontend/vue/components/UserAccount/ClassroomSection.vue
+++ b/frontend/vue/components/UserAccount/ClassroomSection.vue
@@ -5,7 +5,11 @@
         {{ $translate("Classroom") }}
       </template>
       <template #description>
-        {{ $translate("This page shows your classroom activities in the Qiskit Textbook.") }}
+        {{
+          $translate(
+            "This page shows your classroom activities in the Qiskit Textbook."
+          )
+        }}
       </template>
     </UserAccountSectionHeader>
     <div class="classroom__create-syllabus">
@@ -16,7 +20,11 @@
         :segment="createSyllabusCTA.segment"
       />
       <p class="classroom__create-syllabus__description">
-        {{ $translate("Create a curated learning path for your students, using Qiskit Textbook Chapters, Labs, and Summer Schools") }}
+        {{
+          $translate(
+            "Create a curated learning path for your students, using Qiskit Textbook Chapters, Labs, and Summer Schools"
+          )
+        }}
       </p>
     </div>
     <section class="classroom__content">
@@ -24,7 +32,11 @@
         {{ $translate("Active Syllabi") }}
       </h1>
       <p class="classroom__content__description">
-        {{ $translate("Here are your active syllabi. You can edit, publish, and share them with your students") }}
+        {{
+          $translate(
+            "Here are your active syllabi. You can edit, publish, and share them with your students"
+          )
+        }}
       </p>
       <div class="classroom__content__syllabi-list">
         <SyllabusCard
@@ -39,46 +51,45 @@
 </template>
 
 <script lang="ts">
-import { defineComponent } from 'vue-demi'
-import AppCta from '../common/AppCta.vue'
-import { getSyllabi, Syllabus } from '../../../ts/syllabus'
-import UserAccountSectionHeader from './UserAccountSectionHeader.vue'
-import SyllabusCard from './SyllabusCard.vue'
+import { defineComponent } from "vue-demi";
+import AppCta from "../common/AppCta.vue";
+import { getSyllabi, Syllabus } from "../../../ts/syllabus";
+import UserAccountSectionHeader from "./UserAccountSectionHeader.vue";
+import SyllabusCard from "./SyllabusCard.vue";
 
 export default defineComponent({
-  name: 'ClassRoomSection',
+  name: "ClassRoomSection",
   components: {
     UserAccountSectionHeader,
     AppCta,
-    SyllabusCard
+    SyllabusCard,
   },
-  data () {
+  data() {
     return {
-      // TODO: REPLACE MOCK DATA
-      syllabi: ([] as Syllabus[]),
+      syllabi: [] as Syllabus[],
       createSyllabusCTA: {
-        label: this.$translate('Create a Syllabus'),
-        url: '/syllabus/create',
+        label: this.$translate("Create a Syllabus"),
+        url: "/syllabus/create",
         segment: {
-          cta: 'syllabus-create',
-          location: 'user-account-classroom'
-        }
-      }
-    }
+          cta: "syllabus-create",
+          location: "user-account-classroom",
+        },
+      },
+    };
   },
-  mounted () {
+  mounted() {
     getSyllabi().then((syllabi: Syllabus[]) => {
-      this.syllabi = syllabi
-    })
-  }
-})
+      this.syllabi = syllabi;
+    });
+  },
+});
 </script>
 
 <style lang="scss" scoped>
-@import 'carbon-components/scss/globals/scss/typography';
-@import '~/../scss/variables/mq.scss';
-@import '~/../scss/variables/colors.scss';
-@import '~/../scss/mixins/mixins.scss';
+@import "carbon-components/scss/globals/scss/typography";
+@import "~/../scss/variables/mq.scss";
+@import "~/../scss/variables/colors.scss";
+@import "~/../scss/mixins/mixins.scss";
 
 .classroom {
   @include contained();
@@ -95,7 +106,7 @@ export default defineComponent({
     }
 
     &__description {
-      @include type-style('body-long-01');
+      @include type-style("body-long-01");
     }
   }
 
@@ -103,12 +114,12 @@ export default defineComponent({
     padding: $spacing-07 0;
 
     &__title {
-      @include type-style('expressive-heading-04', $fluid: true);
+      @include type-style("expressive-heading-04", $fluid: true);
       margin-bottom: $spacing-05;
     }
 
     &__description {
-      @include type-style('body-long-01');
+      @include type-style("body-long-01");
       margin-bottom: $spacing-07;
     }
 

From c39e7fbfce111db8ace2af9248878a83688f636d Mon Sep 17 00:00:00 2001
From: kifumi <kifumi@jp.ibm.com>
Date: Fri, 10 Jun 2022 09:22:54 +0900
Subject: [PATCH 32/62] update URL of website

I updated the URL to https://qiskit.org/learn/.
---
 .../HowtoTranslate_QiskitTextbook_ja.pdf      | Bin 3320517 -> 3362636 bytes
 1 file changed, 0 insertions(+), 0 deletions(-)

diff --git a/translations/HowtoTranslate_QiskitTextbook_ja.pdf b/translations/HowtoTranslate_QiskitTextbook_ja.pdf
index 634c65acdb1bd4e97b4fbbd3f97a8023d0498e2d..8f738eb4d708fd3554147252bd7bf80e53238342 100644
GIT binary patch
delta 224624
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From 2d5eba6a8cfdc8eefee825b65e8980ba3392c6ca Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Fri, 10 Jun 2022 11:53:56 +0200
Subject: [PATCH 33/62] updated to version 2

---
 package-lock.json | 31487 +++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 30014 insertions(+), 1473 deletions(-)

diff --git a/package-lock.json b/package-lock.json
index 2052f13b9..131f6693e 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -1,8 +1,28443 @@
 {
   "name": "@qiskit/platypus",
   "version": "0.1.1",
-  "lockfileVersion": 1,
+  "lockfileVersion": 2,
   "requires": true,
+  "packages": {
+    "": {
+      "name": "@qiskit/platypus",
+      "version": "0.1.1",
+      "hasInstallScript": true,
+      "license": "Apache-2.0",
+      "dependencies": {
+        "@carbon/colors": "^10.36.0",
+        "@carbon/icons-vue": "~10.48.0",
+        "@carbon/themes": "^11.2.0",
+        "@carbon/vue": "^2.43.1",
+        "@ckeditor/ckeditor5-build-classic": "^34.0.0",
+        "@ckeditor/ckeditor5-vue": "^4.0.1",
+        "@github/clipboard-copy-element": "^1.1.2",
+        "@ibm/plex": "^6.0.2",
+        "@jupyter-widgets/html-manager": "^0.20.1",
+        "@jupyter-widgets/jupyterlab-manager": "^3.1.0",
+        "@jupyterlab/codemirror": "^3.4.2",
+        "@jupyterlab/mathjax2": "^3.4.2",
+        "@jupyterlab/outputarea": "^3.4.2",
+        "@jupyterlab/rendermime": "^3.4.2",
+        "@jupyterlab/services": "^6.4.2",
+        "@lumino/widgets": "^1.31.1",
+        "@mathigon/boost": "^1.1.1",
+        "@mathigon/euclid": "^1.1.1",
+        "@mathigon/studio": "0.1.16",
+        "@qiskit-community/qiskit-vue": "^3.4.0",
+        "@webcomponents/webcomponentsjs": "^2.6.0",
+        "carbon-components": "~10.51.0",
+        "carbon-web-components": "^1.21.0",
+        "class-validator": "^0.13.2",
+        "lit-element": "^2.5.1",
+        "lodash": "^4.17.21",
+        "markdown-it": "^12.2.0",
+        "mongodb": "4.3.1",
+        "nanoid": "^3.3.4",
+        "patch-package": "^6.4.7",
+        "pino": "^7.11.0",
+        "pino-http": "^7.0.0",
+        "pino-pretty": "^7.6.1",
+        "ts-node": "9.1.1",
+        "typescript": "4.5.5",
+        "vue": "~3.1.5",
+        "vue-class-component": "^8.0.0-rc",
+        "vue-router": "4.0.12",
+        "vuedraggable": "^4.1.0",
+        "xml2js": "^0.4.23"
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@@ -1320,17 +29767,17 @@
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@@ -1380,19 +29827,19 @@
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@@ -1407,16 +29854,16 @@
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@@ -1425,14 +29872,14 @@
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@@ -1440,41 +29887,41 @@
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@@ -21716,7 +50255,7 @@
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-          "integrity": "sha1-o7MKXE8ZkYMWeqq5O+764937ZU8=",
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@@ -21820,6 +50359,15 @@
             "ajv-keywords": "^3.1.0"
           }
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+        "string_decoder": {
+          "version": "1.1.1",
+          "resolved": "https://registry.npmjs.org/string_decoder/-/string_decoder-1.1.1.tgz",
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+          "dev": true,
+          "requires": {
+            "safe-buffer": "~5.1.0"
+          }
+        },
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           "resolved": "https://registry.npmjs.org/string-width/-/string-width-3.1.0.tgz",
@@ -21848,19 +50396,10 @@
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-          "resolved": "https://registry.npmjs.org/string_decoder/-/string_decoder-1.1.1.tgz",
-          "integrity": "sha512-n/ShnvDi6FHbbVfviro+WojiFzv+s8MPMHBczVePfUpDJLwoLT0ht1l4YwBCbi8pJAveEEdnkHyPyTP/mzRfwg==",
-          "dev": true,
-          "requires": {
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-          "integrity": "sha1-ajhfuIU9lS1f8F0Oiq+UJ43GPc8=",
+          "integrity": "sha512-VhumSSbBqDTP8p2ZLKj40UjBCV4+v8bUSEpUb4KjRgWk9pbqGF4REFj6KEagidb2f/M6AzC0EmFyDNGaw9OCzg==",
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@@ -21878,7 +50417,7 @@
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-          "integrity": "sha1-fIDBe53+vlmeJzZ+DU3VWQFB2zg=",
+          "integrity": "sha512-ZZWNfCjUokXXDGXFpZehJIkZqq91BcULFq/Pi7M5i4JnxXdhMKAK682z8bCW3o8Hj1wuuzoKcW3DfVzaP6VuNg==",
           "dev": true,
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@@ -22194,9 +50733,10 @@
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-      "resolved": "https://registry.npmjs.org/ws/-/ws-7.5.7.tgz",
-      "integrity": "sha512-KMvVuFzpKBuiIXW3E4u3mySRO2/mCHSyZDJQM5NQ9Q9KHWHWh0NHgfbRMLLrceUK5qAL4ytALJbpRMjixFZh8A=="
+      "version": "7.5.8",
+      "resolved": "https://registry.npmjs.org/ws/-/ws-7.5.8.tgz",
+      "integrity": "sha512-ri1Id1WinAX5Jqn9HejiGb8crfRio0Qgu8+MtL36rlTA6RLsMdWt1Az/19A2Qij6uSHUMphEFaTKa4WG+UNHNw==",
+      "requires": {}
     },
     "xdg-basedir": {
       "version": "4.0.0",
@@ -22246,7 +50786,8 @@
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       "resolved": "https://registry.npmjs.org/xtend/-/xtend-4.0.2.tgz",
-      "integrity": "sha512-LKYU1iAXJXUgAXn9URjiu+MWhyUXHsvfp7mcuYm9dSUKK0/CjtrUwFAxD82/mCWbtLsGjFIad0wIsod4zrTAEQ=="
+      "integrity": "sha512-LKYU1iAXJXUgAXn9URjiu+MWhyUXHsvfp7mcuYm9dSUKK0/CjtrUwFAxD82/mCWbtLsGjFIad0wIsod4zrTAEQ==",
+      "devOptional": true
     },
     "y-codemirror": {
       "version": "3.0.1",
@@ -22375,9 +50916,9 @@
       }
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     "yjs": {
-      "version": "13.5.36",
-      "resolved": "https://registry.npmjs.org/yjs/-/yjs-13.5.36.tgz",
-      "integrity": "sha512-wfB1aCHSp2SKuehmlRK7gOCcpG1hT8uB4X7MZ/suFfgerpgidHYf4j3bjybb5drTTe4Vuqatzc9Bycqh5x2uhg==",
+      "version": "13.5.38",
+      "resolved": "https://registry.npmjs.org/yjs/-/yjs-13.5.38.tgz",
+      "integrity": "sha512-YCHj6DkgxhIRqdxqTI+htGAhvfmgkS974pz+/OOiuLOj0EgGfUKvtp4yYyQGg1Wf3m4oLet9x7gEvCrxaGiVZQ==",
       "requires": {
         "lib0": "^0.2.49"
       }
@@ -22413,7 +50954,7 @@
         "cross-spawn": {
           "version": "5.1.0",
           "resolved": "https://registry.npmjs.org/cross-spawn/-/cross-spawn-5.1.0.tgz",
-          "integrity": "sha1-6L0O/uWPz/b4+UUQoKVUu/ojVEk=",
+          "integrity": "sha512-pTgQJ5KC0d2hcY8eyL1IzlBPYjTkyH72XRZPnLyKus2mBfNjQs3klqbJU2VILqZryAZUt9JOb3h/mWMy23/f5A==",
           "dev": true,
           "requires": {
             "lru-cache": "^4.0.1",
@@ -22424,7 +50965,7 @@
         "execa": {
           "version": "0.8.0",
           "resolved": "https://registry.npmjs.org/execa/-/execa-0.8.0.tgz",
-          "integrity": "sha1-2NdrvBtVIX7RkP1t1J08d07PyNo=",
+          "integrity": "sha512-zDWS+Rb1E8BlqqhALSt9kUhss8Qq4nN3iof3gsOdyINksElaPyNBtKUMTR62qhvgVWR0CqCX7sdnKe4MnUbFEA==",
           "dev": true,
           "requires": {
             "cross-spawn": "^5.0.1",
@@ -22439,7 +50980,7 @@
         "get-stream": {
           "version": "3.0.0",
           "resolved": "https://registry.npmjs.org/get-stream/-/get-stream-3.0.0.tgz",
-          "integrity": "sha1-jpQ9E1jcN1VQVOy+LtsFqhdO3hQ=",
+          "integrity": "sha512-GlhdIUuVakc8SJ6kK0zAFbiGzRFzNnY4jUuEbV9UROo4Y+0Ny4fjvcZFVTeDA4odpFyOQzaw6hXukJSq/f28sQ==",
           "dev": true
         },
         "is-ci": {
@@ -22464,13 +51005,13 @@
         "normalize-path": {
           "version": "1.0.0",
           "resolved": "https://registry.npmjs.org/normalize-path/-/normalize-path-1.0.0.tgz",
-          "integrity": "sha1-MtDkcvkf80VwHBWoMRAY07CpA3k=",
+          "integrity": "sha512-7WyT0w8jhpDStXRq5836AMmihQwq2nrUVQrgjvUo/p/NZf9uy/MeJ246lBJVmWuYXMlJuG9BNZHF0hWjfTbQUA==",
           "dev": true
         },
         "shebang-command": {
           "version": "1.2.0",
           "resolved": "https://registry.npmjs.org/shebang-command/-/shebang-command-1.2.0.tgz",
-          "integrity": "sha1-RKrGW2lbAzmJaMOfNj/uXer98eo=",
+          "integrity": "sha512-EV3L1+UQWGor21OmnvojK36mhg+TyIKDh3iFBKBohr5xeXIhNBcx8oWdgkTEEQ+BEFFYdLRuqMfd5L84N1V5Vg==",
           "dev": true,
           "requires": {
             "shebang-regex": "^1.0.0"
@@ -22479,13 +51020,13 @@
         "shebang-regex": {
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           "resolved": "https://registry.npmjs.org/shebang-regex/-/shebang-regex-1.0.0.tgz",
-          "integrity": "sha1-2kL0l0DAtC2yypcoVxyxkMmO/qM=",
+          "integrity": "sha512-wpoSFAxys6b2a2wHZ1XpDSgD7N9iVjg29Ph9uV/uaP9Ex/KXlkTZTeddxDPSYQpgvzKLGJke2UU0AzoGCjNIvQ==",
           "dev": true
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         "strip-indent": {
           "version": "2.0.0",
           "resolved": "https://registry.npmjs.org/strip-indent/-/strip-indent-2.0.0.tgz",
-          "integrity": "sha1-XvjbKV0B5u1sv3qrlpmNeCJSe2g=",
+          "integrity": "sha512-RsSNPLpq6YUL7QYy44RnPVTn/lcVZtb48Uof3X5JLbF4zD/Gs7ZFDv2HWol+leoQN2mT86LAzSshGfkTlSOpsA==",
           "dev": true
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         "which": {

From 04baa3a034380145033dab16ff2c406bfc4e7f6f Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Fri, 10 Jun 2022 13:24:33 +0200
Subject: [PATCH 34/62] updated package lock to v2

---
 package-lock.json | 137 ++++++++++++++++++++++++++++++++++++++++++----
 1 file changed, 127 insertions(+), 10 deletions(-)

diff --git a/package-lock.json b/package-lock.json
index f8e8cb5d6..2d2768de9 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -37,6 +37,8 @@
         "lit-element": "^2.5.1",
         "lodash": "^4.17.21",
         "markdown-it": "^12.2.0",
+        "mathjax-full": "^3.2.2",
+        "mathjs": "^10.6.1",
         "mongodb": "4.3.1",
         "nanoid": "^3.3.4",
         "patch-package": "^6.4.7",
@@ -7597,6 +7599,18 @@
       "resolved": "https://registry.npmjs.org/commondir/-/commondir-1.0.1.tgz",
       "integrity": "sha512-W9pAhw0ja1Edb5GVdIF1mjZw/ASI0AlShXM83UUGe2DVr5TdAPEA1OA8m/g8zWp9x6On7gqufY+FatDbC3MDQg=="
     },
+    "node_modules/complex.js": {
+      "version": "2.1.1",
+      "resolved": "https://registry.npmjs.org/complex.js/-/complex.js-2.1.1.tgz",
+      "integrity": "sha512-8njCHOTtFFLtegk6zQo0kkVX1rngygb/KQI6z1qZxlFI3scluC+LVTCFbrkWjBv4vvLlbQ9t88IPMC6k95VTTg==",
+      "engines": {
+        "node": "*"
+      },
+      "funding": {
+        "type": "patreon",
+        "url": "https://www.patreon.com/infusion"
+      }
+    },
     "node_modules/component-emitter": {
       "version": "1.3.0",
       "resolved": "https://registry.npmjs.org/component-emitter/-/component-emitter-1.3.0.tgz",
@@ -10447,6 +10461,11 @@
       "resolved": "https://registry.npmjs.org/escape-html/-/escape-html-1.0.3.tgz",
       "integrity": "sha512-NiSupZ4OeuGwr68lGIeym/ksIZMJodUGOSCZ/FSnTxcrekbvqrgdUxlJOMpijaKZVjAJrWrGs/6Jy8OMuyj9ow=="
     },
+    "node_modules/escape-latex": {
+      "version": "1.2.0",
+      "resolved": "https://registry.npmjs.org/escape-latex/-/escape-latex-1.2.0.tgz",
+      "integrity": "sha512-nV5aVWW1K0wEiUIEdZ4erkGGH8mDxGyxSeqPzRNtWP7ataw+/olFObw7hujFWlVjNsaDFw5VZ5NzVSIqRgfTiw=="
+    },
     "node_modules/escape-string-regexp": {
       "version": "4.0.0",
       "resolved": "https://registry.npmjs.org/escape-string-regexp/-/escape-string-regexp-4.0.0.tgz",
@@ -11119,6 +11138,14 @@
         "node": ">=10.13.0"
       }
     },
+    "node_modules/esm": {
+      "version": "3.2.25",
+      "resolved": "https://registry.npmjs.org/esm/-/esm-3.2.25.tgz",
+      "integrity": "sha512-U1suiZ2oDVWv4zPO56S0NcR5QriEahGtdN2OR6FiOG4WJvcjBVFB0qI4+eKoWFH483PKGuLuu6V8Z4T5g63UVA==",
+      "engines": {
+        "node": ">=6"
+      }
+    },
     "node_modules/espree": {
       "version": "9.3.2",
       "resolved": "https://registry.npmjs.org/espree/-/espree-9.3.2.tgz",
@@ -14779,6 +14806,11 @@
       "integrity": "sha512-Yljz7ffyPbrLpLngrMtZ7NduUgVvi6wG9RJ9IUcyCd59YQ911PBJphODUcbOVbqYfxe1wuYf/LJ8PauMRwsM/g==",
       "dev": true
     },
+    "node_modules/javascript-natural-sort": {
+      "version": "0.7.1",
+      "resolved": "https://registry.npmjs.org/javascript-natural-sort/-/javascript-natural-sort-0.7.1.tgz",
+      "integrity": "sha512-nO6jcEfZWQXDhOiBtG2KvKyEptz7RVbpGP4vTD2hLBdmNQSsCiicO2Ioinv6UI4y9ukqnBpy+XZ9H6uLNgJTlw=="
+    },
     "node_modules/javascript-stringify": {
       "version": "2.1.0",
       "resolved": "https://registry.npmjs.org/javascript-stringify/-/javascript-stringify-2.1.0.tgz",
@@ -16016,6 +16048,39 @@
       "resolved": "https://registry.npmjs.org/mathjax/-/mathjax-3.1.2.tgz",
       "integrity": "sha512-BojKspBv4nNWzO1wC6VEI+g9gHDOhkaGHGgLxXkasdU4pwjdO5AXD5M/wcLPkXYPjZ/N+6sU8rjQTlyvN2cWiQ=="
     },
+    "node_modules/mathjax-full": {
+      "version": "3.2.2",
+      "resolved": "https://registry.npmjs.org/mathjax-full/-/mathjax-full-3.2.2.tgz",
+      "integrity": "sha512-+LfG9Fik+OuI8SLwsiR02IVdjcnRCy5MufYLi0C3TdMT56L/pjB0alMVGgoWJF8pN9Rc7FESycZB9BMNWIid5w==",
+      "dependencies": {
+        "esm": "^3.2.25",
+        "mhchemparser": "^4.1.0",
+        "mj-context-menu": "^0.6.1",
+        "speech-rule-engine": "^4.0.6"
+      }
+    },
+    "node_modules/mathjs": {
+      "version": "10.6.1",
+      "resolved": "https://registry.npmjs.org/mathjs/-/mathjs-10.6.1.tgz",
+      "integrity": "sha512-8iZp6uUKKBoCFoUHze9ydsrSji9/IOEzMhwURyoQXaLL1+ILEZnraw4KzZnUBt/XN6lPJPV+7JO94oil3AmosQ==",
+      "dependencies": {
+        "@babel/runtime": "^7.18.3",
+        "complex.js": "^2.1.1",
+        "decimal.js": "^10.3.1",
+        "escape-latex": "^1.2.0",
+        "fraction.js": "^4.2.0",
+        "javascript-natural-sort": "^0.7.1",
+        "seedrandom": "^3.0.5",
+        "tiny-emitter": "^2.1.0",
+        "typed-function": "^2.1.0"
+      },
+      "bin": {
+        "mathjs": "bin/cli.js"
+      },
+      "engines": {
+        "node": ">= 14"
+      }
+    },
     "node_modules/md5-file": {
       "version": "5.0.0",
       "resolved": "https://registry.npmjs.org/md5-file/-/md5-file-5.0.0.tgz",
@@ -16205,6 +16270,11 @@
         "node": ">= 0.6"
       }
     },
+    "node_modules/mhchemparser": {
+      "version": "4.1.1",
+      "resolved": "https://registry.npmjs.org/mhchemparser/-/mhchemparser-4.1.1.tgz",
+      "integrity": "sha512-R75CUN6O6e1t8bgailrF1qPq+HhVeFTM3XQ0uzI+mXTybmphy3b6h4NbLOYhemViQ3lUs+6CKRkC3Ws1TlYREA=="
+    },
     "node_modules/microevent.ts": {
       "version": "0.1.1",
       "resolved": "https://registry.npmjs.org/microevent.ts/-/microevent.ts-0.1.1.tgz",
@@ -16584,6 +16654,11 @@
         "node": ">=0.10.0"
       }
     },
+    "node_modules/mj-context-menu": {
+      "version": "0.6.1",
+      "resolved": "https://registry.npmjs.org/mj-context-menu/-/mj-context-menu-0.6.1.tgz",
+      "integrity": "sha512-7NO5s6n10TIV96d4g2uDpG7ZDpIhMh0QNfGdJw/W47JswFcosz457wqz/b5sAKvl12sxINGFCn80NZHKwxQEXA=="
+    },
     "node_modules/mkdirp": {
       "version": "0.5.6",
       "resolved": "https://registry.npmjs.org/mkdirp/-/mkdirp-0.5.6.tgz",
@@ -22802,6 +22877,11 @@
       "resolved": "https://registry.npmjs.org/secure-json-parse/-/secure-json-parse-2.4.0.tgz",
       "integrity": "sha512-Q5Z/97nbON5t/L/sH6mY2EacfjVGwrCcSi5D3btRO2GZ8pf1K1UN7Z9H5J57hjVU2Qzxr1xO+FmBhOvEkzCMmg=="
     },
+    "node_modules/seedrandom": {
+      "version": "3.0.5",
+      "resolved": "https://registry.npmjs.org/seedrandom/-/seedrandom-3.0.5.tgz",
+      "integrity": "sha512-8OwmbklUNzwezjGInmZ+2clQmExQPvomqjL7LFqOYqtmuxRgQYqOD3mHaU+MvZn5FLUeVxVfQjwLZW/n/JFuqg=="
+    },
     "node_modules/select-hose": {
       "version": "2.0.0",
       "resolved": "https://registry.npmjs.org/select-hose/-/select-hose-2.0.0.tgz",
@@ -23602,6 +23682,27 @@
         "wbuf": "^1.7.3"
       }
     },
+    "node_modules/speech-rule-engine": {
+      "version": "4.0.6",
+      "resolved": "https://registry.npmjs.org/speech-rule-engine/-/speech-rule-engine-4.0.6.tgz",
+      "integrity": "sha512-Hqa4ywf7d3lX2YsnnE8BeEdqFyaTwPSyyVhVGWZlQw4XVh0NCijyVsMZD3I9HsG5JBuDXyRaMVVNZcGJlKbZxA==",
+      "dependencies": {
+        "commander": "9.2.0",
+        "wicked-good-xpath": "1.3.0",
+        "xmldom-sre": "0.1.31"
+      },
+      "bin": {
+        "sre": "bin/sre"
+      }
+    },
+    "node_modules/speech-rule-engine/node_modules/commander": {
+      "version": "9.2.0",
+      "resolved": "https://registry.npmjs.org/commander/-/commander-9.2.0.tgz",
+      "integrity": "sha512-e2i4wANQiSXgnrBlIatyHtP1odfUp0BbV5Y5nEGbxtIrStkEOAAzCUirvLBNXHLr7kwLvJl6V+4V3XV9x7Wd9w==",
+      "engines": {
+        "node": "^12.20.0 || >=14"
+      }
+    },
     "node_modules/split": {
       "version": "0.3.3",
       "resolved": "https://registry.npmjs.org/split/-/split-0.3.3.tgz",
@@ -24867,6 +24968,11 @@
       "integrity": "sha512-qsdtZH+vMoCARQtyod4imc2nIJwg9Cc7lPRrw9CzF8ZKR0khdr8+2nX80PBhET3tcyTtJDxAffGh2rXH4tyU8A==",
       "dev": true
     },
+    "node_modules/tiny-emitter": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/tiny-emitter/-/tiny-emitter-2.1.0.tgz",
+      "integrity": "sha512-NB6Dk1A9xgQPMoGqC5CVXn123gWyte215ONT5Pp5a0yt4nlEoO1ZWeCwpncaekPHXO60i47ihFnZPiRPjRMq4Q=="
+    },
     "node_modules/tmp": {
       "version": "0.2.1",
       "resolved": "https://registry.npmjs.org/tmp/-/tmp-0.2.1.tgz",
@@ -25527,6 +25633,14 @@
         "node": ">= 0.6"
       }
     },
+    "node_modules/typed-function": {
+      "version": "2.1.0",
+      "resolved": "https://registry.npmjs.org/typed-function/-/typed-function-2.1.0.tgz",
+      "integrity": "sha512-bctQIOqx2iVbWGDGPWwIm18QScpu2XRmkC19D8rQGFsjKSgteq/o1hTZvIG/wuDq8fanpBDrLkLq+aEN/6y5XQ==",
+      "engines": {
+        "node": ">= 10"
+      }
+    },
     "node_modules/typed-styles": {
       "version": "0.0.7",
       "resolved": "https://registry.npmjs.org/typed-styles/-/typed-styles-0.0.7.tgz",
@@ -27867,6 +27981,11 @@
       "integrity": "sha1-2e8H3Od7mQK4o6j6SzHD4/fm6Ho=",
       "dev": true
     },
+    "node_modules/wicked-good-xpath": {
+      "version": "1.3.0",
+      "resolved": "https://registry.npmjs.org/wicked-good-xpath/-/wicked-good-xpath-1.3.0.tgz",
+      "integrity": "sha1-gbDpXoZQ5JyUsiKY//hoa1VTz2w="
+    },
     "node_modules/wide-align": {
       "version": "1.1.5",
       "resolved": "https://registry.npmjs.org/wide-align/-/wide-align-1.1.5.tgz",
@@ -28063,6 +28182,14 @@
       "resolved": "https://registry.npmjs.org/xmlchars/-/xmlchars-2.2.0.tgz",
       "integrity": "sha512-JZnDKK8B0RCDw84FNdDAIpZK+JuJw+s7Lz8nksI7SIuU3UXJJslUthsi+uWBUYOwPFwW7W7PRLRfUKpxjtjFCw=="
     },
+    "node_modules/xmldom-sre": {
+      "version": "0.1.31",
+      "resolved": "https://registry.npmjs.org/xmldom-sre/-/xmldom-sre-0.1.31.tgz",
+      "integrity": "sha512-f9s+fUkX04BxQf+7mMWAp5zk61pciie+fFLC9hX9UVvCeJQfNHRHXpeo5MPcR0EUf57PYLdt+ZO4f3Ipk2oZUw==",
+      "engines": {
+        "node": ">=0.1"
+      }
+    },
     "node_modules/xss": {
       "version": "1.0.10",
       "resolved": "https://registry.npmjs.org/xss/-/xss-1.0.10.tgz",
@@ -41123,16 +41250,6 @@
         "seedrandom": "^3.0.5",
         "tiny-emitter": "^2.1.0",
         "typed-function": "^2.1.0"
-      },
-      "dependencies": {
-        "@babel/runtime": {
-          "version": "7.18.3",
-          "resolved": "https://registry.npmjs.org/@babel/runtime/-/runtime-7.18.3.tgz",
-          "integrity": "sha512-38Y8f7YUhce/K7RMwTp7m0uCumpv9hZkitCbBClqQIow1qSbCvGkcegKOXpEWCQLfWmevgRiWokZ1GkpfhbZug==",
-          "requires": {
-            "regenerator-runtime": "^0.13.4"
-          }
-        }
       }
     },
     "md5-file": {

From 79630648ca9f41cb8c840577efac472a5baec6f8 Mon Sep 17 00:00:00 2001
From: Goyo <korgan00@gmail.com>
Date: Fri, 10 Jun 2022 14:41:51 +0200
Subject: [PATCH 35/62] removed logger (#1133)

---
 server/app.ts | 4 ----
 1 file changed, 4 deletions(-)

diff --git a/server/app.ts b/server/app.ts
index a6094deb6..8a7a9cdd8 100644
--- a/server/app.ts
+++ b/server/app.ts
@@ -27,7 +27,6 @@ import { FindSyllabusByCodeController } from './modules/syllabus/commands/find-s
 import { UpdateSyllabusController } from './modules/syllabus/commands/update-syllabus/update-syllabus-controller'
 
 // Logger
-import { loggerExpress } from './libs/logger/logger-express'
 import { logger } from './libs/logger/logger'
 
 const getCourseData = async function (req: Request) {
@@ -126,9 +125,6 @@ const getAccountData = async (req: Request, res: Response) => {
 
 const start = () => {
   new MathigonStudioApp()
-    // Mathigon has the return types incorrect here
-    // @ts-expect-error(2345)
-    .use(loggerExpress)
     .get('/health', (req, res) => res.status(200).send('ok')) // Server Health Checks
     .secure()
     .setup({ sessionSecret: 'project-platypus-beta', csrfBlocklist: ['/profile/accept-policies', '/syllabus'] })

From c9cbf404f9e3e59a9f12b669b14d5754e30e04c4 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Fri, 10 Jun 2022 19:09:55 +0200
Subject: [PATCH 36/62] import -> require

---
 frontend/vue/components/MiniComposer/SymbolicNotation.vue | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/frontend/vue/components/MiniComposer/SymbolicNotation.vue b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
index 8fe1f59c2..2f85b3365 100644
--- a/frontend/vue/components/MiniComposer/SymbolicNotation.vue
+++ b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
@@ -8,7 +8,6 @@
 <script lang="ts">
 import { ref } from '@vue/reactivity'
 import { Vue, prop } from 'vue-class-component'
-import 'mathjax-full/es5/tex-chtml.js'
 
 class Props {
   tex = prop<String>({ default: '', required: true })
@@ -30,6 +29,8 @@ export default class SymbolicNotation extends Vue.with(Props) {
   }
 
   renderTex () {
+    require('mathjax-full/es5/tex-chtml.js')
+
     const MathJax = window.MathJax
     const output = this.output
 

From e7896ad798dab1bbf04c8ee25929052cb7689400 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Fri, 10 Jun 2022 19:58:51 +0200
Subject: [PATCH 37/62] improved visualization

---
 .../vue/components/MiniComposer/gateUtils.ts  | 29 ++++++++++++-------
 1 file changed, 18 insertions(+), 11 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/gateUtils.ts b/frontend/vue/components/MiniComposer/gateUtils.ts
index 0411832c0..ff7afd1fc 100644
--- a/frontend/vue/components/MiniComposer/gateUtils.ts
+++ b/frontend/vue/components/MiniComposer/gateUtils.ts
@@ -230,24 +230,31 @@ export function StateMatrixToTexMatrix (state: StateMatrix) {
   `
 }
 
-const ZERO_KET = '|0\\rangle'
-const ONE_KET = '|1\\rangle'
+function parenthesis (text: string) {
+  return `\\left(${text}\\right)`
+}
+
+function valueKetTex (value: string, ket: 0 | 1) {
+  if (value === '0') {
+    return ''
+  }
+
+  const ketTex = `|${ket}\\rangle`
+  if (value === '1') {
+    return ketTex
+  }
+
+  return `${parenthesis(value)}${ketTex}`
+}
 
 export function StateMatrixToTexKetNotation (state: StateMatrix) {
   const zeroKetValue = StateMatrixElementToTex(state, { x: 0, y: 0 })
   const oneKetValue = StateMatrixElementToTex(state, { x: 1, y: 0 })
 
-  let zeroKetTex = ''
-  let oneKetTex = ''
   const bothKets = zeroKetValue !== '0' && oneKetValue !== '0'
 
-  if (zeroKetValue !== '0') {
-    zeroKetTex = `${bothKets ? '\\left(' : ''}${zeroKetValue === '1' ? '' : zeroKetValue}${bothKets ? '\\right)' : ''}${ZERO_KET}`
-  }
-
-  if (oneKetValue !== '0') {
-    oneKetTex = `${bothKets ? '\\left(' : ''}${oneKetValue === '1' ? '' : oneKetValue}${bothKets ? '\\right)' : ''}${ONE_KET}`
-  }
+  const zeroKetTex = valueKetTex(zeroKetValue, 0)
+  const oneKetTex = valueKetTex(oneKetValue, 1)
 
   let joinTex = ''
   if (bothKets && !oneKetTex.startsWith('-')) {

From a730df6cfd84182b116cada88d0f65b2794d0223 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Fri, 10 Jun 2022 20:13:43 +0200
Subject: [PATCH 38/62] improved parenthesis

---
 frontend/vue/components/MiniComposer/gateUtils.ts | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/frontend/vue/components/MiniComposer/gateUtils.ts b/frontend/vue/components/MiniComposer/gateUtils.ts
index ff7afd1fc..29c863854 100644
--- a/frontend/vue/components/MiniComposer/gateUtils.ts
+++ b/frontend/vue/components/MiniComposer/gateUtils.ts
@@ -244,7 +244,10 @@ function valueKetTex (value: string, ket: 0 | 1) {
     return ketTex
   }
 
-  return `${parenthesis(value)}${ketTex}`
+  const isMultiElement = value.includes('+') || value.lastIndexOf('-') > 1
+  const valueTex = isMultiElement ? parenthesis(value) : value
+
+  return `${valueTex}${ketTex}`
 }
 
 export function StateMatrixToTexKetNotation (state: StateMatrix) {

From 7d8e90318510dc4e3549825ef7908d447cbd336a Mon Sep 17 00:00:00 2001
From: Linxi <107266675+2021-520@users.noreply.github.com>
Date: Sat, 11 Jun 2022 09:52:34 +0800
Subject: [PATCH 39/62] Update LOCALIZATION_CONTRIBUTORS

---
 LOCALIZATION_CONTRIBUTORS | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/LOCALIZATION_CONTRIBUTORS b/LOCALIZATION_CONTRIBUTORS
index 08351df2c..9a2fa10eb 100644
--- a/LOCALIZATION_CONTRIBUTORS
+++ b/LOCALIZATION_CONTRIBUTORS
@@ -63,7 +63,7 @@ Yunzhe Zheng | Dran-Z
 Weixiao Sun | sunwx17
 Bin Liu | fjirsmliu
 Gang Ning | NG-Glen
-
+Mengyin Tan | Linxi
 
 Hindi (HI)
 

From 679f8b1b2c41d554090d22448693b4d1bd2ae308 Mon Sep 17 00:00:00 2001
From: kifumi <kifumi@jp.ibm.com>
Date: Mon, 13 Jun 2022 18:36:04 +0900
Subject: [PATCH 40/62] Update strings.yaml (#1137)

Updated translation of strings.yaml to make it more natural Japanese.

Co-authored-by: Soyoung Shin <63990199+0sophy1@users.noreply.github.com>
---
 translations/ja/strings.yaml | 34 +++++++++++++++++-----------------
 1 file changed, 17 insertions(+), 17 deletions(-)

diff --git a/translations/ja/strings.yaml b/translations/ja/strings.yaml
index 509adac7c..910aa5848 100644
--- a/translations/ja/strings.yaml
+++ b/translations/ja/strings.yaml
@@ -1,8 +1,8 @@
-Advocates: 代弁者
+Advocates: アドボケイト
 Back to course overview: コースの概要に戻る
-Back to textbook home: 教科書ホームに戻るんだ」
-Binary: バイナリ
-Browse all content: コンテンツをすべて参照
+Back to textbook home: テキストブックホームに戻る
+Binary: バイナリー
+Browse all content: すべてのコンテンツを見る
 Circuit: 回路
 Copied!: コピーしました！
 Copy: コピー
@@ -10,32 +10,32 @@ Community: コミュニティー
 Decimal: 10進数
 Description: 解説
 Documentation: ドキュメンテーション
-Drag from here: ここからドラッグ
+Drag from here: ここからドラッグする
 Drop blocks here: ブロックの削除
-Events: 行事
-Eventually, all the vocabulary and mathematics from this section will be shown here. Until then, you can visit the: 最終的に、このセクションのすべての語彙と数学がここに表示されます。 それまでは、
-Gates: ゲイツ
+Events: イベント
+Eventually, all the vocabulary and mathematics from this section will be shown here. Until then, you can visit the: 後ほど、この章のすべての用語と数学がここに表示されるようになります。それまでは以下をご覧ください：
+Gates: ゲート
 Glossary: 用語集
-Hide details: 詳細非表示
+Hide details: 詳細を非表示
 Hide index: インデックスを非表示
 How to read this: これを読む方法
-Keep Going: 立ち止まるな
+Keep Going: 続けます
 Language not yet available: 言語はまだ利用できません
 Learn: 学習
 Lesson Notes: レッスンノート
 Math notations: 数学の表記
-Miss the old version of the textbook? Access it <a href="https://qiskit.org/textbook" onclick="textbook.trackClickEvent('old-textbook-version', 'banner')" target="_blank">here</a>: 古いバージョンの教科書は ? ここで <a href="https://qiskit.org/textbook" onclick="textbook.trackClickEvent('old-textbook-version', 'banner')" target="_blank">ここ</a>にアクセスしてください。
+Miss the old version of the textbook? Access it <a href="https://qiskit.org/textbook" onclick="textbook.trackClickEvent('old-textbook-version', 'banner')" target="_blank">here</a>: 古いバージョンのテキストブックは ? <a href="https://qiskit.org/textbook" onclick="textbook.trackClickEvent('old-textbook-version', 'banner')" target="_blank">ここ</a>にアクセスしてください。
 Next: 次
-Not quite: 完全ではありません
+Not quite: いまいちです
 Notation: 表記
-Nothing here yet: ここには何もない
+Nothing here yet: まだ表示するものがありません
 Overview: 概要
-Run: ラン
+Run: Run
 Show details: 詳細の表示
 Show index: 索引の表示
-That's correct: それは正しいです
+That's correct: 正解です
 Type: タイプ
 Universal frequently used notation: 頻繁に使用される表記法
-universal glossary: ユニバーサル用語集
-Vocabulary: 語彙
+universal glossary: 万能用語集
+Vocabulary: 用語
 What it means: その意味

From 17360390f0f8e8d430970b858de849ec590bd2c5 Mon Sep 17 00:00:00 2001
From: kifumi <kifumi@jp.ibm.com>
Date: Mon, 13 Jun 2022 13:47:15 +0000
Subject: [PATCH 41/62] Translate bernstein-vazirani.ipynb via GitLocalize

---
 .../ja/ch-algorithms/bernstein-vazirani.ipynb | 4420 +++--------------
 1 file changed, 604 insertions(+), 3816 deletions(-)

diff --git a/translations/ja/ch-algorithms/bernstein-vazirani.ipynb b/translations/ja/ch-algorithms/bernstein-vazirani.ipynb
index fefc0c2d6..a74d46df5 100644
--- a/translations/ja/ch-algorithms/bernstein-vazirani.ipynb
+++ b/translations/ja/ch-algorithms/bernstein-vazirani.ipynb
@@ -1,3858 +1,646 @@
 {
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "tags": [
-     "remove_cell"
-    ]
-   },
-   "source": [
-    "# ベルンシュタイン・ヴァジラニ アルゴリズム"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "本節では、まず、ベルンシュタイン・ヴァジラニ問題と、それを解くための古典的アルゴリズムと量子アルゴリズムを紹介します。次に、Qiskitを用いて量子アルゴリズムを実装し、シミュレーターと実デバイス上でそれぞれ実行します。\n",
-    "\n",
-    "## 目次\n",
-    "\n",
-    "1. [ベルンシュタイン・ヴァジラニ アルゴリズム](#algorithm)   \n",
-    "   1.1 [ベルンシュタイン・ヴァジラニ問題](#bvproblem)    \n",
-    "   1.2 [古典的な解法](#classical)   \n",
-    "   1.3 [量子的な解法](#quantum) \n",
-    "2. [具体例](#example)\n",
-    "3. [Qiskitを用いた実装](#implementation)     \n",
-    "   3.1 [シミュレーション](#simulation)     \n",
-    "   3.2 [実デバイス](#device)     \n",
-    "4. [演習](#problems)\n",
-    "5. [参考文献](#references)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 1. ベルンシュタイン・ヴァジラニ アルゴリズム<a id='algorithm'></a>\n",
-    "\n",
-    "参考文献[1]で最初に紹介されたベルンシュタイン・ヴァジラニ アルゴリズムは、前節で取り上げたドイチ・ジョザ アルゴリズムの拡張として見ることができます。このアルゴリズムは、ドイチ・ジョザ問題と比較して、より複雑な問題の計算ツールとして量子コンピューターを使用することに利点があることを示しました。\n",
-    "\n",
-    "### 1.1 ベルンシュタイン・ヴァジラニ問題 <a id='bvproblem'> </a>\n",
-    "\n",
-    "我々は再び、以下のような隠されたブール関数 $f$ を与えられます。この関数は、ビットの文字列を入力として受け取り、$0$ か $1$ のどちらかを返します。\n",
-    "\n",
-    "$f(\\{x_0,x_1,x_2,...\\}) \\rightarrow$ 0または1 ( $x_n$ =0 または 1のとき)\n",
-    "\n",
-    "ドイチ・ジョザ問題のように、均等(balanced)または一定(constant)な関数のどちらかになるのではなく、この関数は入力$x$と文字列$s$のビットごとの内積を返すことが保証されています。つまり、入力$x$について$f(x) = s \\cdot x \\, \\text{(mod 2)}$を満たす関数です。我々は、そのときの$s$を見つけることを期待されています。リバーシブルな古典回路としてのベルンシュタイン・ヴァジラニのオラクルは以下のようにかけます。\n",
-    "    \n",
-    "![classical reversible circuit](images/bv2.svg)\n",
-    "\n",
-    "\n",
-    "\n",
-    "### 1.2 古典的な解法 <a id='classical-solution'> </a>\n",
-    "\n",
-    "古典的には、オラクルは入力 $x$ に対して\n",
-    "$$f_s(x) = s \\cdot x \\mod 2$$ \n",
-    "を返します。\n",
-    "\n",
-    "隠れたビット文字列 $s$ の各ビットは以下の入力のシーケンスをオラクルに問合せすることで洗い出されます。\n",
-    "\n",
-    "|Input(x)|\n",
-    "|:-----:|\n",
-    "|100...0|\n",
-    "|010...0|\n",
-    "|001...0|\n",
-    "|000...1|\n",
-    "\n",
-    "例えば、`x = 1000...0` により $s$ の一番小さい桁のビットをみつけることができます。`x = 0100...0` により $s$ の二番目に小さい桁のビットをみつけることができます。つまり、関数 $f_s(x)$を $n$回呼び出す必要があります。"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### 1.3 量子的な解法 <a id='quantum-solution'> </a>\n",
-    "\n",
-    "量子コンピューターを使うと、関数$f(x)$を1回呼び出すだけで、この問題を100%の確信度で解くことができます。隠れたビット文字列を見つける量子ベルンシュタイン・ヴァジラニ アルゴリズムは非常にシンプルです。\n",
-    "\n",
-    "1. 入力量子ビットを$|0\\rangle^{\\otimes n}$ に、出力量子ビットを$|-\\rangle$状態に初期化\n",
-    "2. アダマールゲートを入力量子ビットに適用\n",
-    "3. オラクルをクエリ\n",
-    "4. 入力レジスタにアダマールゲートを適用\n",
-    "5. 測定\n",
-    "\n",
-    "![Bernstein-Vazirani quantum circuit](images/bv1.svg)\n",
-    "\n",
-    "Tアルゴリズムを説明するために、各量子ビットにアダマールゲートを適用したときに何が起きるのかをみてみましょう。$n$ 量子ビットの量子状態 $|a \\rangle$ にアダマールゲートを適用すると以下の変換をみることができます。\n",
-    "\n",
-    "$$\n",
-    "|a\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} (-1)^{a\\cdot x}|x\\rangle.\n",
-    "$$\n",
-    "\n",
-    "\n",
-    "\n",
-    "<details>\n",
-    "    <summary>式を説明する (クリックして開く)</summary>\n",
-    "アダマールは1つの量子ビットに対して次のような変換を行うことを思い出しましょう。\n",
-    "\n",
-    "$$\n",
-    "H|0\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle)\n",
-    "$$ $$\n",
-    "H|1\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle)\n",
-    "$$\n",
-    "\n",
-    "総和記号を使うことで、以下のように書き換えられます。\n",
-    "\n",
-    "$$\n",
-    "H|a\\rangle = \\sum_{x\\in \\{0,1\\}} (-1)^{a\\cdot x}|x\\rangle.\n",
-    "$$\n",
-    "\n",
-    "2つの量子ビットに対して、それぞれにアダマールを適用すると、次のような変換が行われます。\n",
-    "\n",
-    "$$\n",
-    "H^{\\otimes 2}|00\\rangle = |00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle\n",
-    "$$ $$\n",
-    "H^{\\otimes 2}|01\\rangle = |00\\rangle - |01\\rangle + |10\\rangle - |11\\rangle\n",
-    "$$ $$\n",
-    "H^{\\otimes 2}|10\\rangle = |00\\rangle + |01\\rangle - |10\\rangle - |11\\rangle\n",
-    "$$ $$\n",
-    "H^{\\otimes 2}|11\\rangle = |00\\rangle - |01\\rangle - |10\\rangle + |11\\rangle\n",
-    "$$\n",
-    "\n",
-    "総和記号で、以下のようにまとめて表現することができます。\n",
-    "\n",
-    "$$\n",
-    "H^{\\otimes 2}|a\\rangle = \\sum_{x\\in \\{0,1\\}^2} (-1)^{a\\cdot x}|x\\rangle\n",
-    "$$\n",
-    "\n",
-    "最初の式にたどり着く方法がこれで理解できるかと思います。\n",
-    "</details>\n",
-    "\n",
-    "特に、 $|00...0\\rangle$ に初期化された量子レジスタから始めて、 $n$ 個のアダマールゲートをかけると、おなじみの量子重ね合わせができます。\n",
-    "\n",
-    "$$\n",
-    "|00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} |x\\rangle\n",
-    "$$\n",
-    "\n",
-    "この場合、$a$=0により$(-1)^{a\\cdot x}$ =1となることから、位相$(-1)^{a\\cdot x}$ が消えます。 \n",
-    "\n",
-    "さて、古典のオラクル $f_s$ は、$s \\cdot x\\mod 2 = 1$を満たす任意の入力 $x$ に対して $1$ を、それ以外のときは $0$ を返します。ドイチ・ジョザでも用いた $|{-}\\rangle$に対する位相キックバックのテクニックを利用することで、以下の変換を得られます。\n",
-    "\n",
-    "$$\n",
-    "|x \\rangle \\xrightarrow{f_s} (-1)^{s\\cdot x} |x \\rangle \n",
-    "$$\n",
-    "\n",
-    "隠れた文字列を明らかにするアルゴリズムは、 $|0\\rangle$ のアダマール変換から得られた量子的な重ね合わせで、量子オラクル$f_s$を問い合わせることで、自然に次のようになります。\n",
-    "\n",
-    "$$\n",
-    "|00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} |x\\rangle \\xrightarrow{f_a} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} (-1)^{a\\cdot x}|x\\rangle\n",
-    "$$\n",
-    "\n",
-    "$n$ 個のアダマールゲートの逆行列は、再び $n$ 個のアダマールゲートなので、次のようにして $a$ を求めることができます。\n",
-    "\n",
-    "$$\n",
-    "\\frac{1}{\\sqrt{2^n}} \\sum_{x\\in \\{0,1\\}^n} (-1)^{a\\cdot x}|x\\rangle \\xrightarrow{H^{\\otimes n}} |a\\rangle\n",
-    "$$"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 2. 具体例  <a id='example'></a>\n",
-    "\n",
-    "$n=2$ の量子ビットと秘密の文字列 $s=11$ で具体的な例を見てみましょう。ここでは、参考文献 [2] の定式に従って、1つのレジスタだけを使ってベルンシュタイン・ヴァジラニ量子オラクルのための回路を生成していることに注意してください。 \n",
-    "\n",
-    "<ol>\n",
-    "    <li> 2つの量子ビットのレジスタは0に初期化されています。\n",
-    "    \n",
-    "\n",
-    "$$\\lvert \\psi_0 \\rangle = \\lvert 0 0 \\rangle$$\n",
-    "\n",
-    " \n",
-    "   </li>\n",
-    "\n",
-    "   <li> 両方の量子ビットにアダマールゲートを適用します。\n",
-    "    \n",
-    "\n",
-    "$$\\lvert \\psi_1 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle + \\lvert 0 1 \\rangle + \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right) $$\n",
-    "\n",
-    " \n",
-    "   </li>\n",
-    "\n",
-    "   <li> 文字列 $s=11$ に対して、量子オラクルは以下の演算を行います。\n",
-    "$$\n",
-    "|x \\rangle \\xrightarrow{f_s} (-1)^{x\\cdot 11} |x \\rangle. \n",
-    "$$\n",
-    "\n",
-    "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( (-1)^{00\\cdot 11}|00\\rangle + (-1)^{01\\cdot 11}|01\\rangle + (-1)^{10\\cdot 11}|10\\rangle + (-1)^{11\\cdot 11}|11\\rangle \\right)$$\n",
-    "\n",
-    "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle - \\lvert 0 1 \\rangle - \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)$$\n",
-    "\n",
-    " \n",
-    "   </li>\n",
-    "\n",
-    "   <li> 両方の量子ビットにアダマールゲートを適用します。\n",
-    "    \n",
-    "\n",
-    "$$\\lvert \\psi_3 \\rangle = \\lvert 1 1 \\rangle$$\n",
-    "\n",
-    " \n",
-    "   </li>\n",
-    "\n",
-    "   <li> 秘密の文字列 $s=11$ を見つけるために測定します。\n",
-    "   </li>\n",
-    "\n",
-    "\n",
-    "</ol>\n",
-    "\n",
-    "以下のウィジェット `bv_widget` を活用してください。ボタンを押してそれぞれのステップを適用し、アルゴリズムを実行してみてください。最初の2つの位置引数によって、入力量子ビットの数と秘密の文字列の値を変更することができます。"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
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-      "text/plain": [
-       "HBox(children=(Button(description='H⊗ⁿ', style=ButtonStyle()), Button(description='Oracle', style=ButtonStyle(…"
+      "source": [
+        "# ベルンシュタイン・ヴァジラニ アルゴリズム"
       ]
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-      "text/plain": [
-       "HTMLMath(value='$$ |00\\\\rangle = |00\\\\rangle $$')"
+      "source": [
+        "本節では、まず、ベルンシュタイン・ヴァジラニ問題と、それを解くための古典的アルゴリズムと量子アルゴリズムを紹介します。次に、Qiskitを用いて量子アルゴリズムを実装し、シミュレーターと実デバイス上でそれぞれ実行します。"
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-       "Image(value=b'\\x89PNG\\r\\n\\x1a\\n\\x00\\x00\\x00\\rIHDR\\x00\\x00\\x01*\\x00\\x00\\x00\\xcc\\x08\\x06\\x00\\x00\\x00\\xc4P\\xee\\x0…"
+      "source": [
+        "## 1. ベルンシュタイン・ヴァジラニ アルゴリズム<a id=\"algorithm\"></a>\n",
+        "\n",
+        "参考文献[1]で最初に紹介されたベルンシュタイン・ヴァジラニ アルゴリズムは、前節で取り上げたドイチ・ジョザ アルゴリズムの拡張として見ることができます。このアルゴリズムは、ドイチ・ジョザ問題と比較して、より複雑な問題の計算ツールとして量子コンピューターを使用することに利点があることを示しました。\n",
+        "\n",
+        "### 1.1 ベルンシュタイン・ヴァジラニ問題  <a id=\"bvproblem\"> </a>\n",
+        "\n",
+        "我々は再び、以下のような隠されたブール関数$f$を与えられます。この関数は、ビットの文字列 ($x$) を入力として受け取り、$0$か$1$のどちらかを返します。<br>$$f({x_0,x_1,x_2,...}) \\rightarrow 0 \\textrm{ or } 1 \\textrm{ where } x_n \\textrm{ is }0 \\textrm{ or } 1  $$\n",
+        "\n",
+        "ドイチ・ジョザ問題のように、均等(balanced)または一定(constant)な関数のどちらかになるのではなく、この関数は入力xと文字列sのビットごとの内積を返すことが保証されています。つまり、入力$x$について$f(x) = s \\cdot x , \\text{(mod 2)}$を満たす関数です。我々は、そのときの$s$を見つけることを期待されています。リバーシブルな古典回路としてのベルンシュタイン・ヴァジラニのオラクルは以下のようにかけます。\n",
+        "\n",
+        "![古典的なリバーシブル回路](images/bv2.png)\n",
+        "\n",
+        "### 1.2 古典的な解法 <a id=\"classical-solution\"> </a>\n",
+        "\n",
+        "古典的には、オラクルは入力$x$に対して  $$f_s(x) = s \\cdot x \\mod 2$$ を返します。隠れたビット文字列 $s$ の各ビットは以下の入力のシーケンスをオラクルに問合せすることで洗い出されます。\n",
+        "\n",
+        "Input(x)\n",
+        ":-:\n",
+        "100...0\n",
+        "010...0\n",
+        "001...0\n",
+        "000...1\n",
+        "\n",
+        "例えば、`x = 1000...0`  により $s$ (ビット $s_i$)の一番小さい桁のビットをみつけることができます。`x = 0100...0` により  $s$ の二番目に小さい桁のビットをみつけることができます。つまり、関数$f_s(x)$を $n$ 回呼び出す必要があります "
       ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "from qiskit_textbook.widgets import bv_widget\n",
-    "bv_widget(2, \"11\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 3. Qiskitを用いた実装  <a id='implementation'></a>\n",
-    "\n",
-    "ここで、$s=011$の3量子ビットの関数について、Qiskitでのベルンシュタイン・ヴァジラニ アルゴリズムの実装を見ていきましょう。"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 2,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "# initialization\n",
-    "import matplotlib.pyplot as plt\n",
-    "import numpy as np\n",
-    "\n",
-    "# importing Qiskit\n",
-    "from qiskit import IBMQ, Aer\n",
-    "from qiskit.providers.ibmq import least_busy\n",
-    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, transpile, assemble\n",
-    "\n",
-    "# import basic plot tools\n",
-    "from qiskit.visualization import plot_histogram"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "まず、実験で使用する量子ビット数と、アルゴリズムが求める隠れたビット文字列 $s$ を設定します。隠れたビット文字列 $s$ は、量子オラクルの回路を決定します。"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 3,
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "n = 3 # number of qubits used to represent s\n",
-    "s = '011'   # the hidden binary string"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "その後、Qiskitを使用してベルンシュタイン・ヴァジラニ アルゴリズムをプログラムします。"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 4,
-   "metadata": {},
-   "outputs": [
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+      "source": [
+        "### 1.3 量子的な解法 <a id=\"quantum-solution\"> </a>\n",
+        "\n",
+        "Using a quantum computer, we can solve this problem with 100% confidence after only one call to the function $f(x)$. The quantum Bernstein-Vazirani algorithm to find the hidden bit string is very simple:\n",
+        "\n",
+        "1. 入力量子ビットを$|0\\rangle^{\\otimes n}$ に、出力量子ビットを$|{-}\\rangle$状態に初期化\n",
+        "2. アダマールゲートを入力量子ビットに適用\n",
+        "3. オラクルをクエリ\n",
+        "4. 入力レジスタにアダマールゲートを適用\n",
+        "5. 測定\n",
+        "\n",
+        "<img src=\"images/bv1.png\">\n",
+        "\n",
+        "アルゴリズムを説明するために、各量子ビットにアダマールゲートを適用したときに何が起きるのかをみてみましょう。$n$量子ビットの量子状態$|a\\rangle$ にアダマールゲートを適用すると以下の変換をみることができます。\n",
+        "\n",
+        "$$ |a\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^{a\\cdot x}|x\\rangle. $$\n",
+        "\n",
+        "<details>\n",
+        "    <summary>式を説明する (クリックして開く)</summary>\n",
+        "</details>\n",
+        "\n",
+        "We remember the Hadamard performs the following transformations on one qubit:\n",
+        "\n",
+        "$$ H|0\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) $$ $$ H|1\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle) $$\n",
+        "\n",
+        "総和記号を使うことで、以下のように書き換えられます。\n",
+        "\n",
+        "$$ H|a\\rangle = \\frac{1}{\\sqrt{2}}\\sum_{x\\in {0,1}} (-1)^{a\\cdot x}|x\\rangle. $$\n",
+        "\n",
+        "For two qubits, applying a Hadamard to each performs the following transformations:\n",
+        "\n",
+        "$$ H^{\\otimes 2}|00\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle) $$ $$ H^{\\otimes 2}|01\\rangle = \\tfrac{1}{2}(|00\\rangle - |01\\rangle + |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}|10\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle - |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}|11\\rangle = \\tfrac{1}{2}(|00\\rangle - |01\\rangle - |10\\rangle + |11\\rangle) $$\n",
+        "\n",
+        "総和記号で、以下のようにまとめて表現することができます。\n",
+        "\n",
+        "$$ H^{\\otimes 2}|a\\rangle = \\frac{1}{2}\\sum_{x\\in {0,1}^2} (-1)^{a\\cdot x}|x\\rangle $$\n",
+        "\n",
+        "最初の式にたどり着く方法がこれで理解できるかと思います。\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "特に、$|00\\dots 0\\rangle$に初期化された量子レジスタから始めて、 $n$個のアダマールゲートをかけると、おなじみの量子重ね合わせができます。\n",
+        "\n",
+        "$$ |00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} |x\\rangle $$\n",
+        "\n",
+        "この場合、$a=0$により$(-1)^{a\\cdot x} = 1$ となることから、位相$(-1)^{a\\cdot x}$ が消えます。\n",
+        "\n",
+        "さて、古典のオラクル $f_s$ は、$s \\cdot x\\mod 2 = 1$を満たす任意の入力 $x$ に対して $1$を、それ以外のときは $0$ を返します。ドイチ・ジョザでも用いた$|{-}\\rangle$に対する位相キックバックのテクニックを利用することで、以下の変換を得られます。\n",
+        "\n",
+        "$$ |x \\rangle \\xrightarrow{f_s} (-1)^{s\\cdot x} |x \\rangle $$\n",
+        "\n",
+        "隠れた文字列を明らかにするアルゴリズムは、$|00\\dots 0\\rangle$のアダマール変換から得られた量子的な重ね合わせで、量子オラクル$f_s$を問い合わせることで、自然に次のようになります。\n",
+        "\n",
+        "$$ |00\\dots 0\\rangle \\xrightarrow{H^{\\otimes n}} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} |x\\rangle \\xrightarrow{f_a} \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^{a\\cdot x}|x\\rangle $$\n",
+        "\n",
+        "$n$ 個のアダマールゲートの逆行列は、再び $n$ 個のアダマールゲートなので、次のようにして $a$ を求めることができます。\n",
+        "\n",
+        "$$ \\frac{1}{\\sqrt{2^n}} \\sum_{x\\in {0,1}^n} (-1)^{a\\cdot x}|x\\rangle \\xrightarrow{H^{\\otimes n}} |a\\rangle $$"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 2. 具体例 <a id=\"example\"></a>\n",
+        "\n",
+        "$n=2$ の量子ビットと秘密の文字列 $s=11$ で具体的な例を見てみましょう。ここでは、参考文献 [2] の定式に従って、1つのレジスタだけを使ってベルンシュタイン・ヴァジラニ量子オラクルのための回路を生成していることに注意してください。\n",
+        "\n",
+        "<ol>\n",
+        "    <li> 2つの量子ビットのレジスタは0に初期化されています。</li>\n",
+        "</ol>\n",
+        "\n",
+        "$$\\lvert \\psi_0 \\rangle = \\lvert 0 0 \\rangle$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li> 両方の量子ビットにアダマールゲートを適用します。</li>\n",
+        "\n",
+        "\n",
+        "$$\\lvert \\psi_1 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle + \\lvert 0 1 \\rangle + \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right) $$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>文字列 $s=11$ に対して、量子オラクルは以下の演算を行います。 <br>$$ |x \\rangle \\xrightarrow{f_s} (-1)^{x\\cdot 11} |x \\rangle.  $$</li>\n",
+        "\n",
+        "\n",
+        "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( (-1)^{00\\cdot 11}|00\\rangle + (-1)^{01\\cdot 11}|01\\rangle + (-1)^{10\\cdot 11}|10\\rangle + (-1)^{11\\cdot 11}|11\\rangle \\right)$$\n",
+        "\n",
+        "$$\\lvert \\psi_2 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle - \\lvert 0 1 \\rangle - \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li> 両方の量子ビットにアダマールゲートを適用します。</li>\n",
+        "\n",
+        "\n",
+        "$$\\lvert \\psi_3 \\rangle = \\lvert 1 1 \\rangle$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>秘密の文字列$s=11$ を見つけるために測定します。</li>\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "以下のウィジェット  `bv_widget` を活用してください。ボタンを押してそれぞれのステップを適用し、アルゴリズムを実行してみてください。最初の2つの位置引数によって、入力量子ビットの数と秘密の文字列の値を変更することができます。"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 1,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "4738e4d9713a4204bfa2df6c5179fe2b",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "HBox(children=(Button(description='H⊗ⁿ', style=ButtonStyle()), Button(description='Oracle', style=ButtonStyle(…"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        },
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "aee1e515e0714a978b73ad1fd332945a",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "HTMLMath(value='$$ |00\\\\rangle = |00\\\\rangle $$')"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        },
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "0392b76bb3674157aa5c1f8d0836ec3e",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "Image(value=b'\\x89PNG\\r\\n\\x1a\\n\\x00\\x00\\x00\\rIHDR\\x00\\x00\\x00\\xce\\x00\\x00\\x00\\xcc\\x08\\x06\\x00\\x00\\x00;\\xd7\\x9c…"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
       ],
-      "text/plain": [
-       "<Figure size 840.392x325.08 with 1 Axes>"
+      "source": [
+        "from qiskit_textbook.widgets import bv_widget\n",
+        "bv_widget(2, \"11\")"
       ]
-     },
-     "execution_count": 4,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# We need a circuit with n qubits, plus one ancilla qubit\n",
-    "# Also need n classical bits to write the output to\n",
-    "bv_circuit = QuantumCircuit(n+1, n)\n",
-    "\n",
-    "# put ancilla in state |->\n",
-    "bv_circuit.h(n)\n",
-    "bv_circuit.z(n)\n",
-    "\n",
-    "# Apply Hadamard gates before querying the oracle\n",
-    "for i in range(n):\n",
-    "    bv_circuit.h(i)\n",
-    "    \n",
-    "# Apply barrier \n",
-    "bv_circuit.barrier()\n",
-    "\n",
-    "# Apply the inner-product oracle\n",
-    "s = s[::-1] # reverse s to fit qiskit's qubit ordering\n",
-    "for q in range(n):\n",
-    "    if s[q] == '0':\n",
-    "        bv_circuit.i(q)\n",
-    "    else:\n",
-    "        bv_circuit.cx(q, n)\n",
-    "        \n",
-    "# Apply barrier \n",
-    "bv_circuit.barrier()\n",
-    "\n",
-    "#Apply Hadamard gates after querying the oracle\n",
-    "for i in range(n):\n",
-    "    bv_circuit.h(i)\n",
-    "\n",
-    "# Measurement\n",
-    "for i in range(n):\n",
-    "    bv_circuit.measure(i, i)\n",
-    "\n",
-    "bv_circuit.draw()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### 3a. シミュレーターでの実験   <a id='simulation'></a>\n",
-    "\n",
-    "上記の回路をシミュレーター上で実行できます。"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 5,
-   "metadata": {
-    "scrolled": false
-   },
-   "outputs": [
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 3. Qiskitを用いた実装  <a id=\"implementation\"></a>\n",
+        "\n",
+        "ここで、$s=011$の3量子ビットの関数について、Qiskitでのベルンシュタイン・ヴァジラニ アルゴリズムの実装を見ていきましょう。"
+      ]
+    },
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+      "cell_type": "code",
+      "execution_count": 2,
+      "metadata": {
+      },
+      "outputs": [
+
       ],
-      "text/plain": [
-       "<Figure size 504x360 with 1 Axes>"
+      "source": [
+        "# initialization\n",
+        "import matplotlib.pyplot as plt\n",
+        "import numpy as np\n",
+        "\n",
+        "# importing Qiskit\n",
+        "from qiskit import IBMQ, Aer\n",
+        "from qiskit.providers.ibmq import least_busy\n",
+        "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, transpile\n",
+        "\n",
+        "# import basic plot tools\n",
+        "from qiskit.visualization import plot_histogram"
       ]
-     },
-     "execution_count": 5,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# use local simulator\n",
-    "aer_sim = Aer.get_backend('aer_simulator')\n",
-    "shots = 1024\n",
-    "qobj = assemble(bv_circuit)\n",
-    "results = aer_sim.run(qobj).result()\n",
-    "answer = results.get_counts()\n",
-    "\n",
-    "plot_histogram(answer)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "測定の結果は、隠れた文字列 `011` であることがわかります。"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "### 3b. 実デバイスでの実験 <a id='device'></a>\n",
-    "\n",
-    "以下のように実デバイス上で回路を動作させることができます。"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 6,
-   "metadata": {
-    "tags": [
-     "uses-hardware"
-    ]
-   },
-   "outputs": [
+    },
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "least busy backend:  ibmq_london\n"
-     ]
-    }
-   ],
-   "source": [
-    "# Load our saved IBMQ accounts and get the least busy backend device with less than or equal to 5 qubits\n",
-    "IBMQ.load_account()\n",
-    "provider = IBMQ.get_provider(hub='ibm-q')\n",
-    "provider.backends()\n",
-    "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits <= 5 and\n",
-    "                                   x.configuration().n_qubits >= 2 and\n",
-    "                                   not x.configuration().simulator and x.status().operational==True))\n",
-    "print(\"least busy backend: \", backend)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "metadata": {
-    "tags": [
-     "uses-hardware"
-    ]
-   },
-   "outputs": [
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "まず、実験で使用する量子ビット数と、アルゴリズムが求める隠れたビット文字列 $s$を設定します。隠れたビット文字列 $s$ は、量子オラクルの回路を決定します。 "
+      ]
+    },
     {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Job Status: job has successfully run\n"
-     ]
-    }
-   ],
-   "source": [
-    "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n",
-    "from qiskit.tools.monitor import job_monitor\n",
-    "\n",
-    "shots = 1024\n",
-    "transpiled_bv_circuit = transpile(bv_circuit, backend)\n",
-    "job = backend.run(transpiled_bv_circuit, shots=shots)\n",
-    "\n",
-    "job_monitor(job, interval=2)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "metadata": {
-    "tags": [
-     "uses-hardware"
-    ]
-   },
-   "outputs": [
+      "cell_type": "code",
+      "execution_count": 3,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "n = 3 # number of qubits used to represent s\n",
+        "s = '011'   # the hidden binary string"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "その後、Qiskitを使用してベルンシュタイン・ヴァジラニ アルゴリズムをプログラムします。"
+      ]
+    },
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+            ],
+            "text/plain": [
+              "<Figure size 748.797x325.08 with 1 Axes>"
+            ]
+          },
+          "execution_count": 4,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
       ],
-      "text/plain": [
-       "<Figure size 504x360 with 1 Axes>"
+      "source": [
+        "# We need a circuit with n qubits, plus one auxiliary qubit\n",
+        "# Also need n classical bits to write the output to\n",
+        "bv_circuit = QuantumCircuit(n+1, n)\n",
+        "\n",
+        "# put auxiliary in state |->\n",
+        "bv_circuit.h(n)\n",
+        "bv_circuit.z(n)\n",
+        "\n",
+        "# Apply Hadamard gates before querying the oracle\n",
+        "for i in range(n):\n",
+        "    bv_circuit.h(i)\n",
+        "    \n",
+        "# Apply barrier \n",
+        "bv_circuit.barrier()\n",
+        "\n",
+        "# Apply the inner-product oracle\n",
+        "s = s[::-1] # reverse s to fit qiskit's qubit ordering\n",
+        "for q in range(n):\n",
+        "    if s[q] == '0':\n",
+        "        bv_circuit.i(q)\n",
+        "    else:\n",
+        "        bv_circuit.cx(q, n)\n",
+        "        \n",
+        "# Apply barrier \n",
+        "bv_circuit.barrier()\n",
+        "\n",
+        "#Apply Hadamard gates after querying the oracle\n",
+        "for i in range(n):\n",
+        "    bv_circuit.h(i)\n",
+        "\n",
+        "# Measurement\n",
+        "for i in range(n):\n",
+        "    bv_circuit.measure(i, i)\n",
+        "\n",
+        "bv_circuit.draw()"
       ]
-     },
-     "execution_count": 8,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "# Get the results from the computation\n",
-    "results = job.result()\n",
-    "answer = results.get_counts()\n",
-    "\n",
-    "plot_histogram(answer)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "見ての通り、ほとんどの結果は`011`です。他の結果は量子計算の誤差によるものです。"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 4. 演習 <a id='problems'></a>\n",
-    "\n",
-    "1. 以下のウィジットを使用してベルンシュタイン・ヴァジラニ アルゴリズムが異なるオラクルで動く様子を確認してください。"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 9,
-   "metadata": {},
-   "outputs": [
+    },
     {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "94208c824e9f4267b7d336986115d5ec",
-       "version_major": 2,
-       "version_minor": 0
+      "cell_type": "markdown",
+      "metadata": {
       },
-      "text/plain": [
-       "HBox(children=(Button(description='H⊗ⁿ', style=ButtonStyle()), Button(description='Oracle', style=ButtonStyle(…"
+      "source": [
+        "### 3a. シミュレーターでの実験  <a id=\"simulation\"></a>\n",
+        "\n",
+        "上記の回路をシミュレーター上で実行できます。 "
       ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
     },
     {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "1a9e3c846d7443569f0a72fd7e2d16c7",
-       "version_major": 2,
-       "version_minor": 0
+      "cell_type": "code",
+      "execution_count": 5,
+      "metadata": {
+        "scrolled": false
       },
-      "text/plain": [
-       "HTMLMath(value='$$ |000\\\\rangle = |000\\\\rangle $$')"
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 5,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# use local simulator\n",
+        "aer_sim = Aer.get_backend('aer_simulator')\n",
+        "shots = 1024\n",
+        "results = aer_sim.run(bv_circuit).result()\n",
+        "answer = results.get_counts()\n",
+        "\n",
+        "plot_histogram(answer)"
       ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
     },
     {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "6c0ceaa4301d4a3a80c04cc008430557",
-       "version_major": 2,
-       "version_minor": 0
+      "cell_type": "markdown",
+      "metadata": {
       },
-      "text/plain": [
-       "Image(value=b'\\x89PNG\\r\\n\\x1a\\n\\x00\\x00\\x00\\rIHDR\\x00\\x00\\x01*\\x00\\x00\\x01\\x08\\x08\\x06\\x00\\x00\\x00\\xe8^\\xb9\\x1…"
+      "source": [
+        "測定の結果が隠された文字列 `011` であることが分かります。 "
       ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "from qiskit_textbook.widgets import bv_widget\n",
-    "bv_widget(3, \"011\", hide_oracle=False)"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "2. 上記のベルンシュタイン・ヴァジラニの[実装](#implementation)は、秘密のビット文字列$s = 011$の場合のものです。秘密の文字列 $s = 1011$ の場合を実装してください。結果は期待通りでしたか？説明してみてください。\n",
-    "\n",
-    "3. 上記のベルンシュタイン・ヴァジラニの[実装](#implementation)は、秘密のビット文字列$s = 011$の場合のものです。秘密の文字列 $s = 1110110101$ の場合を実装してください。結果は期待通りでしたか？説明してみてください。"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 5. 参考文献 <a id='references'></a>\n",
-    "1. Ethan Bernstein and Umesh Vazirani (1997) \"Quantum Complexity Theory\" SIAM Journal on Computing, Vol. 26, No. 5: 1411-1473, [doi:10.1137/S0097539796300921](https://doi.org/10.1137/S0097539796300921).\n",
-    "2. Jiangfeng Du, Mingjun Shi, Jihui Wu, Xianyi Zhou, Yangmei Fan, BangJiao Ye, Rongdian Han (2001) \"Implementation of a quantum algorithm to solve the Bernstein-Vazirani parity problem without entanglement on an ensemble quantum computer\", Phys. Rev. A 64, 042306, [10.1103/PhysRevA.64.042306](https://doi.org/10.1103/PhysRevA.64.042306), [arXiv:quant-ph/0012114](https://arxiv.org/abs/quant-ph/0012114). "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "metadata": {},
-   "outputs": [
+    },
     {
-     "data": {
-      "text/plain": [
-       "{'qiskit-terra': '0.14.2',\n",
-       " 'qiskit-aer': '0.5.2',\n",
-       " 'qiskit-ignis': '0.3.3',\n",
-       " 'qiskit-ibmq-provider': '0.7.2',\n",
-       " 'qiskit-aqua': '0.7.3',\n",
-       " 'qiskit': '0.19.6'}"
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 3b. 実デバイスでの実験 <a id=\"device\"></a>\n",
+        "\n",
+        "以下のように実デバイス上で回路を動作させることができます。"
       ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "import qiskit.tools.jupyter\n",
-    "%qiskit_version_table"
-   ]
-  }
- ],
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+      "metadata": {
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         ]
-       }
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "least busy backend:  ibmq_quito\n"
+          ]
+        }
+      ],
+      "source": [
+        "# Load our saved IBMQ accounts and get the least busy backend device with less than or equal to 5 qubits\n",
+        "IBMQ.load_account()\n",
+        "provider = IBMQ.get_provider(hub='ibm-q')\n",
+        "provider.backends()\n",
+        "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits <= 5 and\n",
+        "                                   x.configuration().n_qubits >= 2 and\n",
+        "                                   not x.configuration().simulator and x.status().operational==True))\n",
+        "print(\"least busy backend: \", backend)"
+      ]
+    },
+    {
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+      "execution_count": 7,
+      "metadata": {
+        "tags": [
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+        ]
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+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Job Status: job has successfully run\n"
+          ]
+        }
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-        "encoding": "base64",
-        "path": [
-         "value"
+      "source": [
+        "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n",
+        "from qiskit.tools.monitor import job_monitor\n",
+        "\n",
+        "shots = 1024\n",
+        "transpiled_bv_circuit = transpile(bv_circuit, backend)\n",
+        "job = backend.run(transpiled_bv_circuit, shots=shots)\n",
+        "\n",
+        "job_monitor(job, interval=2)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 8,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
         ]
-       }
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 8,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# Get the results from the computation\n",
+        "results = job.result()\n",
+        "answer = results.get_counts()\n",
+        "\n",
+        "plot_histogram(answer)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "見ての通り、ほとんどの結果は`011`です。他の結果は量子計算の誤差によるものです。 "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 4. 演習 <a id=\"problems\"></a>\n",
+        "\n",
+        "1. 以下のウィジットを使用してベルンシュタイン・ヴァジラニ アルゴリズムが異なるオラクルで動く様子を確認してください。"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 9,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "50aab689dcab494488d8ca5be416d30e",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "HBox(children=(Button(description='H⊗ⁿ', style=ButtonStyle()), Button(description='Oracle', style=ButtonStyle(…"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        },
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "9de25e0347754d70a79689270d19b1bb",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "HTMLMath(value='$$ |000\\\\rangle = |000\\\\rangle $$')"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        },
+        {
+          "data": {
+            "application/vnd.jupyter.widget-view+json": {
+              "model_id": "d34999a9c17949b4ac75bb46bc01c603",
+              "version_major": 2,
+              "version_minor": 0
+            },
+            "text/plain": [
+              "Image(value=b'\\x89PNG\\r\\n\\x1a\\n\\x00\\x00\\x00\\rIHDR\\x00\\x00\\x00\\xce\\x00\\x00\\x01\\x08\\x08\\x06\\x00\\x00\\x00\\x17\\xd9\\…"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "from qiskit_textbook.widgets import bv_widget\n",
+        "bv_widget(3, \"011\", hide_oracle=False)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "1. 上記のベルンシュタイン・ヴァジラニの [実装](#implementation) は、秘密のビット文字列$s = 011$の場合のものです。秘密の文字列 $s = 1011$ の場合を実装してください。結果は期待通りでしたか？説明してみてください。\n",
+        "2. 上記のベルンシュタイン・ヴァジラニの [実装](#implementation) は、秘密のビット文字列$s = 011$の場合のものです。秘密の文字列 $s = 11101101$ の場合を実装してください。結果は期待通りでしたか？説明してみてください。"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 5. 参考文献 <a id=\"references\"></a>\n",
+        "\n",
+        "1. Ethan Bernstein and Umesh Vazirani (1997) \"Quantum Complexity Theory\" SIAM Journal on Computing, Vol. 26, No. 5: 1411-1473, [doi:10.1137/S0097539796300921](https://doi.org/10.1137/S0097539796300921).\n",
+        "2. Jiangfeng Du, Mingjun Shi, Jihui Wu, Xianyi Zhou, Yangmei Fan, BangJiao Ye, Rongdian Han (2001) \"Implementation of a quantum algorithm to solve the Bernstein-Vazirani parity problem without entanglement on an ensemble quantum computer\", Phys. Rev. A 64, 042306, [10.1103/PhysRevA.64.042306](https://doi.org/10.1103/PhysRevA.64.042306), [arXiv:quant-ph/0012114](https://arxiv.org/abs/quant-ph/0012114). "
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 10,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "name": "stderr",
+          "output_type": "stream",
+          "text": [
+            "/usr/local/anaconda3/envs/terra-unstable/lib/python3.9/site-packages/qiskit/aqua/__init__.py:86: DeprecationWarning: The package qiskit.aqua is deprecated. It was moved/refactored to qiskit-terra For more information see <https://github.com/Qiskit/qiskit-aqua/blob/main/README.md#migration-guide>\n",
+            "  warn_package('aqua', 'qiskit-terra')\n"
+          ]
+        },
+        {
+          "data": {
+            "text/html": [
+              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.19.0</td></tr><tr><td><code>qiskit-aer</code></td><td>0.9.1</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.6.0</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.17.0</td></tr><tr><td><code>qiskit-aqua</code></td><td>0.9.5</td></tr><tr><td><code>qiskit</code></td><td>0.31.0</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.9.7</td></tr><tr><td>Python compiler</td><td>Clang 10.0.0 </td></tr><tr><td>Python build</td><td>default, Sep 16 2021 08:50:36</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>32.0</td></tr><tr><td colspan='2'>Fri Nov 05 14:14:51 2021 GMT</td></tr></table>"
+            ],
+            "text/plain": [
+              "<IPython.core.display.HTML object>"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
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-       "description": "Clear",
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-     "fa650588f9694b1aa84160d58a085eb5": {
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-      }
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+      "source": [
+        "import qiskit.tools.jupyter\n",
+        "%qiskit_version_table"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
     },
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-   }
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 2
 }

From 4af62e7126c781ff673309177c0a52f3292165c4 Mon Sep 17 00:00:00 2001
From: Daiki Murata <d.murata0623@gmail.com>
Date: Mon, 13 Jun 2022 13:47:16 +0000
Subject: [PATCH 42/62] Translate bernstein-vazirani.ipynb via GitLocalize

---
 translations/ja/ch-algorithms/bernstein-vazirani.ipynb | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/translations/ja/ch-algorithms/bernstein-vazirani.ipynb b/translations/ja/ch-algorithms/bernstein-vazirani.ipynb
index a74d46df5..bce1f136f 100644
--- a/translations/ja/ch-algorithms/bernstein-vazirani.ipynb
+++ b/translations/ja/ch-algorithms/bernstein-vazirani.ipynb
@@ -57,7 +57,7 @@
       "source": [
         "### 1.3 量子的な解法 <a id=\"quantum-solution\"> </a>\n",
         "\n",
-        "Using a quantum computer, we can solve this problem with 100% confidence after only one call to the function $f(x)$. The quantum Bernstein-Vazirani algorithm to find the hidden bit string is very simple:\n",
+        "量子コンピューターを使うと、関数 $f(x)$を1回呼び出すだけで、この問題を100%の確度で解くことができます。隠れたビット文字列を見つける量子ベルンシュタイン・ヴァジラニ アルゴリズムは非常にシンプルです。\n",
         "\n",
         "1. 入力量子ビットを$|0\\rangle^{\\otimes n}$ に、出力量子ビットを$|{-}\\rangle$状態に初期化\n",
         "2. アダマールゲートを入力量子ビットに適用\n",
@@ -75,7 +75,7 @@
         "    <summary>式を説明する (クリックして開く)</summary>\n",
         "</details>\n",
         "\n",
-        "We remember the Hadamard performs the following transformations on one qubit:\n",
+        "アダマールゲートは1つの量子ビットに対して次のような変換を行うことを思い出しましょう。\n",
         "\n",
         "$$ H|0\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle + |1\\rangle) $$ $$ H|1\\rangle = \\tfrac{1}{\\sqrt{2}}(|0\\rangle - |1\\rangle) $$\n",
         "\n",
@@ -83,7 +83,7 @@
         "\n",
         "$$ H|a\\rangle = \\frac{1}{\\sqrt{2}}\\sum_{x\\in {0,1}} (-1)^{a\\cdot x}|x\\rangle. $$\n",
         "\n",
-        "For two qubits, applying a Hadamard to each performs the following transformations:\n",
+        "2つの量子ビットに対して、それぞれにアダマールゲートを適用すると、次のような変換が行われます。\n",
         "\n",
         "$$ H^{\\otimes 2}|00\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle + |10\\rangle + |11\\rangle) $$ $$ H^{\\otimes 2}|01\\rangle = \\tfrac{1}{2}(|00\\rangle - |01\\rangle + |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}|10\\rangle = \\tfrac{1}{2}(|00\\rangle + |01\\rangle - |10\\rangle - |11\\rangle) $$ $$ H^{\\otimes 2}|11\\rangle = \\tfrac{1}{2}(|00\\rangle - |01\\rangle - |10\\rangle + |11\\rangle) $$\n",
         "\n",

From cd7827bda699cf382aa228318e4fcf68cc34bcdc Mon Sep 17 00:00:00 2001
From: kifumi <kifumi@jp.ibm.com>
Date: Mon, 13 Jun 2022 14:08:25 +0000
Subject: [PATCH 43/62] Translate defining-quantum-circuits.ipynb via
 GitLocalize

---
 .../defining-quantum-circuits.ipynb           | 261 +++++++++---------
 1 file changed, 125 insertions(+), 136 deletions(-)

diff --git a/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb b/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb
index 9cacb7ca0..e0b09f2ec 100644
--- a/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb
+++ b/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb
@@ -1,139 +1,128 @@
 {
- "cells": [
-  {
-   "cell_type": "markdown",
-   "metadata": {
-    "tags": [
-     "remove_cell"
-    ]
-   },
-   "source": [
-    "# 量子回路"
-   ]
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "tags": [
+          "remove_cell"
+        ]
+      },
+      "source": [
+        "# 量子回路"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 目次\n",
+        "\n",
+        "1. [はじめに](#intro)\n",
+        "2. [量子回路とは何か?](#whatis)\n",
+        "3. [例: 量子テレポーテーション](#teleportation)\n",
+        "4. [例: 変分量子固有値ソルバー](#vqe)\n",
+        "5. [なぜ部分的に古典なのか?](#why-classical)\n",
+        "\n",
+        "## 1. はじめに <a id=\"intro\"></a>\n",
+        "\n",
+        "これまでに、様々な [単一量子ビット](https://qiskit.org/textbook/ch-states/single-qubit-gates.html) ゲートや [複数量子ビット](https://qiskit.org/textbook/ch-gates/introduction.html) ゲートを見てきました。また、これらのゲートを他の部品と組み合わせて量子回路を構築する方法も見てきました。\n",
+        "\n",
+        "量子アルゴリズムを実装するために量子回路を構築するので、実際の量子コンピューターに量子アルゴリズムを実装する前に、具体的に量子回路の定義を強調しておきます。\n",
+        "\n",
+        "## 2. 量子回路とは何か?  <a id=\"whatis\"></a>\n",
+        "\n",
+        "量子回路とは、  *量子データ(量子ビットなど)に対するコヒーレントな量子演算と、リアルタイム同時古典計算 で構成される計算ルーチンのことです*。量子回路は、 *量子ゲート 、* *測定 、 リセット* の順序立てられたシーケンスであり、これらはすべてリアルタイム古典計算のデータを使用した条件付ゲートが作用することがあります。\n",
+        "\n",
+        "量子データの任意のユニタリ変換が、集合内のゲートのシーケンスと同様に任意に効率的に近似できる場合、量子ゲートの集合は [ユニバーサル(普遍的)](https://qiskit.org/textbook/ch-gates/proving-universality.html) であると言われています。任意の量子プログラムは、量子回路と非連続古典計算のシーケンスで表現することができます。\n",
+        "\n",
+        "## 3. 例: 量子テレポーテーション <a id=\"teleportation\"></a>\n",
+        "\n",
+        "以下の量子回路を見てください 次の章では [量子テレポーテーションアルゴリズム](https://qiskit.org/textbook/ch-algorithms/teleportation.html) の実装を学びます。今のところ，量子回路の構成要素を見れば十分です。\n",
+        "\n",
+        "![Quantum Teleportation Labeled](images/teleportation_labelled.svg)\n",
+        "\n",
+        "量子回路は3つの量子ビットと2つの古典ビットを使っています。この量子回路には主に4つのコンポーネントがあります。\n",
+        "\n",
+        "### 初期化とリセット\n",
+        "\n",
+        "まず、量子状態を定義して量子計算を開始する必要があります。これは、初期化とリセット操作を使用して実現されます。リセットは単一量子ゲートと、測定によって目的の状態を正常に作成できたかどうかをモニターするリアルタイムの古典的な同時計算の組み合わせによって実行することができます。$q_0$ から所望の状態 $\\vert\\psi\\rangle$ への初期化には次に単一量子ビットゲートを適応します。\n",
+        "\n",
+        "### 量子ゲート\n",
+        "\n",
+        "第二に、テレポーテーションアルゴリズムで必要とされるように、3つの量子ビットを操作する一連の量子ゲートを適用します。この場合、1量子ビットのアダマールゲート($H$)と2ビットの制御Xゲート($\\oplus$)を適用するだけでよいです。\n",
+        "\n",
+        "### 測定\n",
+        "\n",
+        "第三に、3つの量子ビットのうち2つの量子ビットを測定します。古典コンピューターは、各量子ビットの測定値を古典的な結果(0と1)として解釈し、2つの古典ビットに格納します。\n",
+        "\n",
+        "### 古典条件付ゲート\n",
+        "\n",
+        "第四に、3番目の量子ビットに単一量子ビットゲートの$Z$と$X$を適用します。これらのゲートは、2つの古典ビットに格納されている各測定結果が1の場合それぞれ作用します。この場合、古典計算の結果を、同じ量子回路内でリアルタイムに同時使用しています。"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 4. 例: 変分量子固有値ソルバー<a id=\"vqe\"></a>\n",
+        "\n",
+        "ここに量子プログラムの例を示します。次の章では、このプログラムが [変分量子固有値ソルバー](https://qiskit.org/textbook/ch-applications/vqe-molecules.html) を実装していることを説明します。このプログラムでは、古典的なコンピューターと量子コンピューターが *非並行* に動作します．\n",
+        "\n",
+        "![Variational Quantum Eigensolver Labeled](https://github.com/Qiskit/platypus/blob/main/translations/ja/ch-algorithms/images/vqe-labeled.png?raw=true)\n",
+        "\n",
+        "### 量子ブロック\n",
+        "\n",
+        "上記の例1と同様に、単一量子ビットゲートと複数量子ビットゲートを用いたリセット処理の組み合わせにより、量子状態|$\\vert\\Psi(\\theta)\\rangle$を準備します。ここでは、状態のパラメーターは$\\theta$<br>で設定されます。一度準備された量子状態は、量子ゲートを使って操作され、測定されます。量子ブロック内のすべての操作は量子回路で構成されています。\n",
+        "\n",
+        "### 古典ブロック\n",
+        "\n",
+        "量子状態が測定されると、古典コンピューターは、測定結果を解釈し、目的のアプリケーションのために選択されたコスト関数を使用して、そのコストを計算します。このコストに基づいて、古典的なコンピューターは、パラメーター $\\theta$ の別の値を決定します。\n",
+        "\n",
+        "### 処理の組み合わせ\n",
+        "\n",
+        "古典的なコンピューターが次のパラメーター $\\theta$ を決定すると、一連のリセットと単一量子ビットゲート、複数量子ビットゲートを量子回路で使用して $\\vert\\Psi(\\theta)\\rangle$ を準備し、このプロセスは測定された量子状態のコストが安定するまで、または別の事前に定められた結果と合致するまで続けられます。"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 5. なぜ部分的に古典なのか?  <a id=\"why-classical\"></a>\n",
+        "\n",
+        "ユニバーサルな量子コンピューターは古典的なコンピューターができることは何でもできますが、量子状態は壊れやすいので、量子回路に古典的な部分を追加することがよくあります。\n",
+        "\n",
+        "量子ビットを測定すると、その状態が崩れ、多くの情報が破壊されてしまいます。測定は情報を破壊するだけなので、理論的には常に最後に測定すれば計算上の優位性を失うことはありません。実際には、早期に測定することで、多くの実用的な利点が得られます。\n",
+        "\n",
+        "例えば、テレポーテーション回路では、量子チャネルの代わりに古典チャネルで情報を送ることができるように、量子ビットを測定しています。量子チャネルを作成するのが非常に難しいため、量子情報を他の人に送信する方法がない一方で、古典的なチャネルは非常に安定しています。\n",
+        "\n",
+        "In the variational quantum eigensolver example, splitting the computation up into smaller quantum computations actually loses us some computational advantage, but makes up for this on noisy hardware by reducing the time our qubits are in superposition. This means there is less chance interference will introduce inaccuracies in our results.\n",
+        "\n",
+        "最後に、量子計算の結果を古典的な日常の世界で使うためには、計算の最後にこれらの状態を測定して解釈する必要があります。\n"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
   },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 目次\n",
-    "\n",
-    "1. [導入](#intro)\n",
-    "2. [量子回路とは何か?](#whatis)\n",
-    "3. [例: 量子テレポーテーション](#teleportation)\n",
-    "4. [例: 変分量子固有値ソルバー](#vqe)\n",
-    "5. [なぜ部分的に古典なのか?](#why-classical)\n",
-    "\n",
-    "## 1. 導入 <a id='intro'></a>\n",
-    "これまでに、様々な[単一量子ビットゲート](../ch-states/single-qubit-gates.html)や[複数量子ビットゲート](../ch-gates/introduction.html)を見てきました。また、これらのゲートを他の部品と組み合わせて量子回路を構築する方法も見てきました。\n",
-    "\n",
-    "量子アルゴリズムを実装するために量子回路を構築するので、実際の量子コンピューターに量子アルゴリズムを実装する前に、具体的に量子回路の定義を強調しておきます。\n",
-    "\n",
-    "\n",
-    "## 2. 量子回路とは何か? <a id='whatis'></a>\n",
-    "\n",
-    "量子回路とは、 _量子データ(量子ビットなど)に対するコヒーレントな量子演算と、リアルタイム同時古典計算_ で構成される計算ルーチンのことです。量子回路は、 _量子ゲート_ 、 _測定_ 、 _リセット_ の順序立てられたシーケンスであり、これらはすべてリアルタイム古典計算のデータを使用した条件付ゲートが作用することがあります。\n",
-    "\n",
-    "量子データの任意のユニタリ変換が、集合内のゲートのシーケンスと同様に任意に効率的に近似できる場合、量子ゲートの集合は[ユニバーサル(普遍的)](../ch-gates/proving-universality.html)であると言われています。任意の量子プログラムは、量子回路と非連続古典計算のシーケンスで表現することができます。\n",
-    "\n",
-    "\n",
-    "## 3. 量子テレポーテーション <a id='teleportation'></a>\n",
-    "\n",
-    "以下の量子回路を見てください 次の章では[量子テレポーテーションアルゴリズム](../ch-algorithms/teleportation.html)の実装を学びます。今のところ，量子回路の構成要素を見れば十分です。\n",
-    "\n",
-    "![Quantum Teleportation Labeled](images/teleportation-labeled.png)\n",
-    "\n",
-    "量子回路は3つの量子ビットと2つの古典ビットを使っています。この量子回路には主に4つのコンポーネントがあります。\n",
-    "\n",
-    "### 初期化とリセット\n",
-    "まず、量子状態を定義して量子計算を開始する必要があります。これは、初期化とリセット操作を使用して実現されます。リセットは単一量子ゲートと、測定によって目的の状態を正常に作成できたかどうかをモニターするリアルタイムの古典的な同時計算の組み合わせによって実行することができます。$q_0$から所望の状態$\\vert\\psi\\rangle$への初期化には次に単一量子ビットゲートを適応します。\n",
-    "\n",
-    "### 量子ゲート\n",
-    "第二に、テレポーテーションアルゴリズムで必要とされるように、3つの量子ビットを操作する一連の量子ゲートを適用します。この場合、1量子ビットのアダマールゲート($H$)と2ビットの制御Xゲート($\\oplus$)を適用するだけでよいです。\n",
-    "\n",
-    "### 測定\n",
-    "第三に、3つの量子ビットのうち2つの量子ビットを測定します。古典コンピューターは、各量子ビットの測定値を古典的な結果(0と1)として解釈し、2つの古典ビットに格納します。\n",
-    "\n",
-    "### 古典条件付ゲート\n",
-    "第四に、3番目の量子ビットに単一量子ビットゲートの$Z$と$X$を適用します。これらのゲートは、2つの古典ビットに格納されている各測定結果が1の場合それぞれ作用します。この場合、古典計算の結果を、同じ量子回路内でリアルタイムに同時使用しています。"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 4.例: 変分量子固有値ソルバー <a id='vqe'></a>\n",
-    "\n",
-    "ここに量子プログラムの例を示します。次の章では、このプログラムが[変分量子固有値ソルバー](../ch-applications/vqe-molecules.html)を実装していることを説明します。このプログラムでは、古典的なコンピューターと量子コンピューターが _非並行_ に動作します．\n",
-    "\n",
-    "![Variational Quantum Eigensolver Labeled](images/vqe-labeled.png)\n",
-    "\n",
-    "### 量子ブロック\n",
-    "上記の例1と同様に、単一量子ビットゲートと複数量子ビットゲートを用いたリセット処理の組み合わせにより、量子状態$\\vert\\Psi(\\theta)\\rangle$を準備します。ここでは、状態のパラメーターは$\\theta$で設定されます。一度準備された量子状態は、量子ゲートを使って操作され、測定されます。量子ブロック内のすべての操作は量子回路で構成されています。\n",
-    "\n",
-    "### 古典ブロック\n",
-    "量子状態が測定されると、古典コンピューターは、測定結果を解釈し、目的のアプリケーションのために選択されたコスト関数を使用して、そのコストを計算します。このコストに基づいて、古典的なコンピューターは、パラメーター$\\theta$の別の値を決定します。\n",
-    "\n",
-    "### 処理の組み合わせ\n",
-    "古典的なコンピューターが次のパラメーター$\\theta$を決定すると、一連のリセットと単一量子ビットゲート、複数量子ビットゲートを量子回路で使用して$\\vert\\Psi(\\theta)\\rangle$を準備し、このプロセスは測定された量子状態のコストが安定するまで、または別の事前に定められた結果と合致するまで続けられます。"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "metadata": {},
-   "source": [
-    "## 5. なぜ部分的に古典なのか? <a id='why-classical'></a>\n",
-    "\n",
-    "ユニバーサルな量子コンピューターは古典的なコンピューターができることは何でもできますが、量子状態は壊れやすいので、量子回路に古典的な部分を追加することがよくあります。\n",
-    "\n",
-    "量子ビットを測定すると、その状態が崩れ、多くの情報が破壊されてしまいます。測定は情報を破壊するだけなので、理論的には常に最後に測定すれば計算上の優位性を失うことはありません。実際には、早期に測定することで、多くの実用的な利点が得られます。\n",
-    "\n",
-    "例えば、テレポーテーション回路では、量子チャネルの代わりに古典チャネルで情報を送ることができるように、量子ビットを測定しています。量子チャネルを作成するのが非常に難しいため、量子情報を他の人に送信する方法がない一方で、古典的なチャネルは非常に安定しています。\n",
-    "\n",
-    "変分量子固有値ソルバーの例では、計算をより小さな量子計算に分割することで、計算上の優位性が失われますが、ノイズの多いハードウェアでは、量子ビットの重ね合わせ時間を減らすことで、その分を補うことができます。これは、干渉が結果に不正確さをもたらす可能性が低いことを意味します。\n",
-    "\n",
-    "最後に、量子計算の結果を古典的な日常の世界で使うためには、計算の最後にこれらの状態を測定して解釈する必要があります。"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
-   "outputs": [],
-   "source": []
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.8.5"
-  },
-  "toc": {
-   "base_numbering": 1,
-   "nav_menu": {},
-   "number_sections": true,
-   "sideBar": true,
-   "skip_h1_title": false,
-   "title_cell": "Table of Contents",
-   "title_sidebar": "Contents",
-   "toc_cell": false,
-   "toc_position": {},
-   "toc_section_display": true,
-   "toc_window_display": false
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 2
+  "nbformat": 4,
+  "nbformat_minor": 2
 }

From d18ac58816721a68f7a7acff53ff5830af3ed675 Mon Sep 17 00:00:00 2001
From: Daiki Murata <d.murata0623@gmail.com>
Date: Mon, 13 Jun 2022 14:08:26 +0000
Subject: [PATCH 44/62] Translate defining-quantum-circuits.ipynb via
 GitLocalize

---
 translations/ja/ch-algorithms/defining-quantum-circuits.ipynb | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb b/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb
index e0b09f2ec..6fcae2750 100644
--- a/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb
+++ b/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb
@@ -40,7 +40,7 @@
         "\n",
         "以下の量子回路を見てください 次の章では [量子テレポーテーションアルゴリズム](https://qiskit.org/textbook/ch-algorithms/teleportation.html) の実装を学びます。今のところ，量子回路の構成要素を見れば十分です。\n",
         "\n",
-        "![Quantum Teleportation Labeled](images/teleportation_labelled.svg)\n",
+        "![ラベル付けされた量子テレポーテーション](images/teleportation_labelled.svg)\n",
         "\n",
         "量子回路は3つの量子ビットと2つの古典ビットを使っています。この量子回路には主に4つのコンポーネントがあります。\n",
         "\n",
@@ -98,7 +98,7 @@
         "\n",
         "例えば、テレポーテーション回路では、量子チャネルの代わりに古典チャネルで情報を送ることができるように、量子ビットを測定しています。量子チャネルを作成するのが非常に難しいため、量子情報を他の人に送信する方法がない一方で、古典的なチャネルは非常に安定しています。\n",
         "\n",
-        "In the variational quantum eigensolver example, splitting the computation up into smaller quantum computations actually loses us some computational advantage, but makes up for this on noisy hardware by reducing the time our qubits are in superposition. This means there is less chance interference will introduce inaccuracies in our results.\n",
+        "変分量子固有値ソルバーの例では、計算をより小さな量子計算に分割することで、計算上の優位性が失われますが、ノイズの多いハードウェアでは、量子ビットの重ね合わせ時間を減らすことで、その分を補うことができます。これは、干渉が結果に不正確さをもたらす可能性が低いことを意味します。\n",
         "\n",
         "最後に、量子計算の結果を古典的な日常の世界で使うためには、計算の最後にこれらの状態を測定して解釈する必要があります。\n"
       ]

From 9ca22eae7b222167e6b496bf8ff5338c18b1b1f3 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Mon, 13 Jun 2022 16:15:24 +0200
Subject: [PATCH 45/62] added explanation text and changed example with block

---
 .../MiniComposer/CircuitSandboxWidget.vue     | 56 +++++++++----------
 notebooks/examples/widgets.ipynb              | 15 +++--
 2 files changed, 36 insertions(+), 35 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index a493ba6a4..bb76450d1 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -27,6 +27,10 @@
         :max-gates="MAX_GATES"
       />
     </div>
+    <div
+      ref="explanationRef"
+      class="mini-composer__explanation"
+    />
     <div class="mini-composer__state-views">
       <section class="mini-composer__state-views__view">
         <h1 class="mini-composer__state-views__view__title">
@@ -85,10 +89,8 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   get configDiv () { return (this.configRef as unknown as HTMLDivElement) }
   instructionsRef = ref<HTMLDivElement | null>(null)
   get instructions () { return (this.instructionsRef as unknown as HTMLDivElement) }
-  footerInfoRef = ref<HTMLDivElement | null>(null)
-  get footerInfoDiv () { return (this.footerInfoRef as unknown as HTMLDivElement) }
-  lessonRef = ref<HTMLDivElement | null>(null)
-  get lessonDiv () { return (this.lessonRef as unknown as HTMLDivElement) }
+  explanationRef = ref<HTMLDivElement | null>(null)
+  get explanation () { return (this.explanationRef as unknown as HTMLDivElement) }
 
   MAX_GATES = 7
   correctSolution = SolutionState.CORRECT
@@ -122,28 +124,28 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
 
   mounted () {
     const instructionElement = this.configDiv.querySelector('.instructions')
-    const circuitElement = this.configDiv.querySelector('.circuit')
+    const explanationElement = this.configDiv.querySelector('.explanation')
+    const availableGatesElement = this.configDiv.querySelector('.availableGates')
 
-    this.setCircuitConfig(circuitElement as HTMLElement)
+    this.setCircuitConfig(availableGatesElement as HTMLElement)
 
     if (instructionElement) {
       this.instructions.appendChild(instructionElement)
     } else {
       this.instructions.remove()
     }
+    if (explanationElement) {
+      this.explanation.appendChild(explanationElement)
+    } else {
+      this.explanation.remove()
+    }
   }
 
-  setCircuitConfig (htmlConfigElement: HTMLElement) {
-    this.autoMeasureGate = !!htmlConfigElement.querySelector('.autoMeasureGate')
-
-    const availableGatesElement = htmlConfigElement.querySelector('.availableGates') as HTMLElement
+  setCircuitConfig (availableGatesElement: HTMLElement) {
     this.initialAvailableGates = []
     if (availableGatesElement && availableGatesElement.textContent) {
       this.initialAvailableGates = this.stringToGateNameArray(availableGatesElement.textContent)
     }
-
-    const initialCircuitElement = Array.from<HTMLElement>(htmlConfigElement.querySelectorAll('.initialCircuit .qubit'))
-    this.circuitState = this.htmlElementsToCircuit(initialCircuitElement)
   }
 
   stringToGateNameArray (text: string) : ComposerGate[] {
@@ -160,15 +162,6 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
       })
   }
 
-  htmlElementsToCircuit (elements: HTMLElement[]) : ComposerGate[][] {
-    return elements.map((qubitLine: HTMLElement) => {
-      if (qubitLine.textContent === null) {
-        return []
-      }
-      return this.stringToGateNameArray(qubitLine.textContent)
-    })
-  }
-
   onRestartButton () {
 
   }
@@ -183,19 +176,21 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
 .mini-composer {
   display: grid;
   grid-template-columns: 20rem 1fr;
-  grid-template-rows: min-content min-content 1fr;
+  grid-template-rows: min-content min-content 1fr min-content;
   grid-template-areas:
     "text text"
     "gates lesson"
-    "circuit lesson";
+    "circuit lesson"
+    "explanation lesson";
 
   @include mq ($until: medium) {
     grid-template-columns: 1fr;
-    grid-template-rows: min-content min-content min-content min-content;
+    grid-template-rows: repeat(5, min-content);
     grid-template-areas:
       "text"
       "gates"
       "circuit"
+      "explanation"
       "lesson";
   }
 
@@ -204,12 +199,15 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   }
 
   &__exercise-text {
+    @include type-style('body-long-01');
     grid-area: text;
     border-bottom: 1px solid $border-color;
-
-    ::v-deep(.carousel__selector) {
-      margin-top: 0;
-    }
+    padding: $spacing-05;
+  }
+  &__explanation {
+    @include type-style('body-long-01');
+    grid-area: explanation;
+    padding: $spacing-05;
   }
   &__gates {
     grid-area: gates;
diff --git a/notebooks/examples/widgets.ipynb b/notebooks/examples/widgets.ipynb
index 82ec2f30e..19dec7446 100644
--- a/notebooks/examples/widgets.ipynb
+++ b/notebooks/examples/widgets.ipynb
@@ -13,14 +13,17 @@
    "source": [
     "## Circuit sandbox\n",
     "\n",
+    "<!-- ::: q-block -->\n",
+    "\n",
+    "### Amplitude encoding\n",
+    "\n",
     "    q-circuit-sandbox-widget(goal=\"circuit-sandbox\")\n",
     "        .slide\n",
-    "            .circuit\n",
-    "                .availableGates H X Z Y T S\n",
-    "                .initialCircuit\n",
-    "                    .qubit\n",
-    "            .instructions first slide instructions\n",
-    "\n"
+    "            .availableGates H X Z Y T S\n",
+    "            .instructions Text here establishing what this widget is, how the user can use it, and what we intend them to use it for. Lorem ipsum dolor sit amet, consectetur adipiscing elit, lorem ipsum dolor sit amet, consectetur.\n",
+    "            .explanation Text here to explain the difference between the matrix view and the state vector view\n",
+    "\n",
+    "<!-- ::: -->\n"
    ]
   },
   {

From e99c92896ac0e890e78574b992ef790da2c5a281 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Mon, 13 Jun 2022 16:27:26 +0200
Subject: [PATCH 46/62] improved example code and added goal to widget

---
 .../vue/components/MiniComposer/CircuitSandboxWidget.vue | 6 +++++-
 notebooks/examples/widgets.ipynb                         | 9 ++++-----
 2 files changed, 9 insertions(+), 6 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index bb76450d1..f6282f3c9 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -107,6 +107,10 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   lastGateId = 0
 
   get matrixState () {
+    if (this.goal && this.circuitState[0].length > 0) {
+      this.$step?.score(this.goal as string)
+    }
+
     return this.circuitState[0].reduce((prev, current) => {
       return gateMatrix(current).apply(prev)
     }, IdentityState())
@@ -163,7 +167,7 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   }
 
   onRestartButton () {
-
+    this.circuitState = [[]]
   }
 }
 </script>
diff --git a/notebooks/examples/widgets.ipynb b/notebooks/examples/widgets.ipynb
index 19dec7446..ef15d9750 100644
--- a/notebooks/examples/widgets.ipynb
+++ b/notebooks/examples/widgets.ipynb
@@ -15,13 +15,12 @@
     "\n",
     "<!-- ::: q-block -->\n",
     "\n",
-    "### Amplitude encoding\n",
+    "### Circuit sandbox\n",
     "\n",
     "    q-circuit-sandbox-widget(goal=\"circuit-sandbox\")\n",
-    "        .slide\n",
-    "            .availableGates H X Z Y T S\n",
-    "            .instructions Text here establishing what this widget is, how the user can use it, and what we intend them to use it for. Lorem ipsum dolor sit amet, consectetur adipiscing elit, lorem ipsum dolor sit amet, consectetur.\n",
-    "            .explanation Text here to explain the difference between the matrix view and the state vector view\n",
+    "        .availableGates H X Z Y T S\n",
+    "        .instructions Text here establishing what this widget is, how the user can use it, and what we intend them to use it for. Lorem ipsum dolor sit amet, consectetur adipiscing elit, lorem ipsum dolor sit amet, consectetur.\n",
+    "        .explanation Text here to explain the difference between the matrix view and the state vector view\n",
     "\n",
     "<!-- ::: -->\n"
    ]

From 9993d93a0ab7350e6438ac49e649e122a9d565c7 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Mon, 13 Jun 2022 16:34:43 +0200
Subject: [PATCH 47/62] cleaned code

---
 .../MiniComposer/CircuitSandboxWidget.vue     | 25 ++++---------------
 1 file changed, 5 insertions(+), 20 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index f6282f3c9..4155d544c 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -22,7 +22,7 @@
       </h1>
       <Circuit
         :circuit-state="circuitState"
-        :auto-measure-gate="autoMeasureGate"
+        :auto-measure-gate="false"
         :max-lines="circuitState.length"
         :max-gates="MAX_GATES"
       />
@@ -58,10 +58,7 @@
 import { ref } from '@vue/reactivity'
 import { Options, Vue, prop } from 'vue-class-component'
 import draggable from 'vuedraggable'
-import Carousel from '../Carousel/Carousel.vue'
-import KetCircuitLine from '../Sketch/KetCircuitLine.vue'
-import AppCta from '../common/AppCta.vue'
-import SolutionStateIndicator, { SolutionState } from '../common/SolutionStateIndicator.vue'
+import SolutionStateIndicator from '../common/SolutionStateIndicator.vue'
 import GatesPool from './GatesPool.vue'
 import Circuit from './Circuit.vue'
 import { ComposerGate, gateMatrix } from './composerTypes'
@@ -74,12 +71,9 @@ class Props {
 
 @Options({
   components: {
-    Carousel,
-    KetCircuitLine,
     Circuit,
     GatesPool,
     draggable,
-    AppCta,
     SymbolicNotation,
     SolutionStateIndicator
   }
@@ -93,9 +87,6 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   get explanation () { return (this.explanationRef as unknown as HTMLDivElement) }
 
   MAX_GATES = 7
-  correctSolution = SolutionState.CORRECT
-
-  autoMeasureGate: boolean = false
 
   initialAvailableGates: ComposerGate[] = []
   get availableGates (): ComposerGate[] {
@@ -104,8 +95,6 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
 
   circuitState: ComposerGate[][] = [[]]
 
-  lastGateId = 0
-
   get matrixState () {
     if (this.goal && this.circuitState[0].length > 0) {
       this.$step?.score(this.goal as string)
@@ -123,8 +112,6 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   get stateVectorTex () {
     return StateMatrixToTexKetNotation(this.matrixState)
   }
-  // stateVectorTex = 'x = {-b \\pm \\sqrt{b^2-4ac} \\over 2a}'
-  // stateVectorTex = '({\\sqrt{1} \\over 4} + {\\sqrt{1} \\over 4} + {\\sqrt{1} \\over 4} |0\\rangle) + ({\\sqrt{1} \\over 4} + {\\sqrt{1} \\over 4} + {\\sqrt{1} \\over 4}|1\\rangle)'
 
   mounted () {
     const instructionElement = this.configDiv.querySelector('.instructions')
@@ -153,6 +140,7 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   }
 
   stringToGateNameArray (text: string) : ComposerGate[] {
+    let lastGateId = 0
     return text.split(' ')
       .filter(text => text !== '')
       .map<ComposerGate>((gateText: string) => {
@@ -160,9 +148,9 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
           const parts = gateText.split('(')
           const gateName = parts[0]
           const rotation = parts[1]?.split(')')[0]
-          return { name: gateName as GateName, id: this.lastGateId++, rotation }
+          return { name: gateName as GateName, id: lastGateId++, rotation }
         }
-        return { name: GateName.UNKNOWN, id: this.lastGateId++ }
+        return { name: GateName.UNKNOWN, id: lastGateId++ }
       })
   }
 
@@ -256,9 +244,6 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
           }
         }
       }
-      &__z-gate {
-        flex: 0 0 auto;
-      }
     }
   }
   &__state-views {

From 6a26c1a85d30041e2687dfda021af28cd41dca64 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Mon, 13 Jun 2022 17:31:37 +0200
Subject: [PATCH 48/62] fixed size to avoid overflow

---
 frontend/vue/components/MiniComposer/SymbolicNotation.vue | 6 +++++-
 1 file changed, 5 insertions(+), 1 deletion(-)

diff --git a/frontend/vue/components/MiniComposer/SymbolicNotation.vue b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
index 2f85b3365..0acc17b68 100644
--- a/frontend/vue/components/MiniComposer/SymbolicNotation.vue
+++ b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
@@ -36,8 +36,9 @@ export default class SymbolicNotation extends Vue.with(Props) {
 
     MathJax.startup.promise.then(() => {
       MathJax.texReset()
+      const outputMetrics = MathJax.getMetricsFor(output)
       const options = {
-        ...MathJax.getMetricsFor(output),
+        ...outputMetrics,
         ...{ display: true }
       }
       MathJax
@@ -49,6 +50,9 @@ export default class SymbolicNotation extends Vue.with(Props) {
           output.appendChild(node)
           MathJax.startup.document.clear()
           MathJax.startup.document.updateDocument()
+          if (outputMetrics.containerWidth < node.clientWidth) {
+            node.style.fontSize = `${(outputMetrics.containerWidth / node.clientWidth) * 100}%`
+          }
         }).catch((err: Error) => {
           // If there was an error, put the message into the output instead
           output.appendChild(document.createElement('pre')).appendChild(document.createTextNode(err.message))

From 008de449dcb9fad7aab912369366ae41680f9bbc Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Mon, 13 Jun 2022 17:37:53 +0200
Subject: [PATCH 49/62] improved size on overflow

---
 frontend/vue/components/MiniComposer/SymbolicNotation.vue | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/frontend/vue/components/MiniComposer/SymbolicNotation.vue b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
index 0acc17b68..f3be1424e 100644
--- a/frontend/vue/components/MiniComposer/SymbolicNotation.vue
+++ b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
@@ -51,7 +51,7 @@ export default class SymbolicNotation extends Vue.with(Props) {
           MathJax.startup.document.clear()
           MathJax.startup.document.updateDocument()
           if (outputMetrics.containerWidth < node.clientWidth) {
-            node.style.fontSize = `${(outputMetrics.containerWidth / node.clientWidth) * 100}%`
+            node.style.fontSize = `${(outputMetrics.containerWidth / node.clientWidth) * 100 * 1.1}%`
           }
         }).catch((err: Error) => {
           // If there was an error, put the message into the output instead

From 455e875223fb709c651256b919ea40fce1fb59a5 Mon Sep 17 00:00:00 2001
From: Sumin Jin <nineil91@naver.com>
Date: Tue, 14 Jun 2022 13:01:53 +0900
Subject: [PATCH 50/62] Update LOCALIZATION_CONTRIBUTORS

---
 LOCALIZATION_CONTRIBUTORS | 1 +
 1 file changed, 1 insertion(+)

diff --git a/LOCALIZATION_CONTRIBUTORS b/LOCALIZATION_CONTRIBUTORS
index 3b47b548e..0c998f1b1 100644
--- a/LOCALIZATION_CONTRIBUTORS
+++ b/LOCALIZATION_CONTRIBUTORS
@@ -43,6 +43,7 @@ Sungjoo Hwang | Denny-Hwang
 Dayeong Kang | tula3and
 Mingi Ryu | mingiryu
 Young Ju Tak | glucktak
+Sumin Jin | nineil91
 
 Indonesian (ID)
 

From 3119920f28b9c2b62934c57d36c3d77b53eb2bae Mon Sep 17 00:00:00 2001
From: kifumi <kifumi@jp.ibm.com>
Date: Tue, 14 Jun 2022 04:21:29 +0000
Subject: [PATCH 51/62] Translate encoding.ipynb via GitLocalize

---
 .../quantum-machine-learning/encoding.ipynb   | 593 ++++++++++++++++++
 1 file changed, 593 insertions(+)
 create mode 100644 translations/ja/quantum-machine-learning/encoding.ipynb

diff --git a/translations/ja/quantum-machine-learning/encoding.ipynb b/translations/ja/quantum-machine-learning/encoding.ipynb
new file mode 100644
index 000000000..33248f127
--- /dev/null
+++ b/translations/ja/quantum-machine-learning/encoding.ipynb
@@ -0,0 +1,593 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "gloss": {
+          "computational-basis-state": {
+            "text": "Also known as Z-basis states, these are the states we measure when we measure in the Z (or 'computational') basis. These are the states with labels like |00〉 and |00110100〉. IBM systems always measure in the Z-basis.",
+            "title": "computational basis state"
+          },
+          "features": {
+            "text": "A feature is a property of the things we're trying to learn about that we can assign a number to. If we were learning something about cats, the features might be \"height\" or \"age\" or \"propensity to consume treats\".",
+            "title": "features"
+          },
+          "unitary": {
+            "text": "A unitary operation is a reversible operation that preserves the norm (i.e. makes sure our probabilities always sum to 1). <a href='https://en.wikipedia.org/wiki/Unitary_matrix'>Read more</a>.",
+            "title": "unitary"
+          }
+        }
+      },
+      "source": [
+        "# データの符号化\n",
+        "\n",
+        "このページでは、量子機械学習のためのデータ符号化の問題を紹介し、さまざまなデータ符号化手法について説明し、実装します。 "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## はじめに\n",
+        "\n",
+        "機械学習モデルを成功させるには、データの表現が非常に重要です。古典的な機械学習の場合では、データをいかに数値的に表現し、古典的な機械学習アルゴリズムで最適に処理できるようにするかが問題となります。\n",
+        "\n",
+        "量子機械学習の場合、問題は似ていますが、より基本的です：問題は、データをどうやって表現して、量子システムに効率的に入力し、量子機械学習アルゴリズムで処理できるようにするかです。これは通常、データの符号化（データ *エンコーディング* ）と呼ばれますが、データの *埋め込み* または *ロード* とも呼ばれます。\n",
+        "\n",
+        "このプロセスは、量子機械学習アルゴリズムの重要な部分であり、その計算能力に直接影響します。 "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "formulas": {
+          "_ket-dataset": {
+            "meaning": "This is a quantum statevector that represents our dataset, 𝒳.",
+            "say": "Ket script X"
+          },
+          "_ket-x": {
+            "meaning": "This vertical bar and angled bracket mean we're referring to a <a href='https://en.wikipedia.org/wiki/Bra%E2%80%93ket_notation'>ket</a> (column vector) with label 'x'.",
+            "say": "Ket x"
+          },
+          "_m": {
+            "meaning": "This is the number of entries in our dataset."
+          },
+          "_sum-m": {
+            "meaning": "This notation means we add together |x<sup>m</sup>〉 (the m<sup>th</sup> element of our dataset) for all values of m between 1 and M (i.e., the entire dataset).",
+            "say": "Sum of all computational basis states in our dataset (𝒳)"
+          },
+          "_x-lil-m": {
+            "meaning": "This is the m<sup>th</sup> element of the dataset. It is an N-dimensional vector. Here, the 'm' is just used to mean \"any number between 1 and M\"",
+            "say": "X little-M"
+          },
+          "brace": {
+            "meaning": "These curly brackets (braces) mean everything inside the brackets forms a <a href='https://en.wikipedia.org/wiki/Set_(mathematics)'>set</a>.",
+            "say": "Brace (or \"curly bracket\")",
+            "type": "Universal notation"
+          },
+          "ellipsis": {
+            "meaning": "These dots omit things where the pattern can be implied.",
+            "say": "Ellipsis",
+            "type": "Universal notation"
+          },
+          "in": {
+            "meaning": "This symbol means the things to the left of the symbol are contained in the set to the right of the symbol.",
+            "say": "In",
+            "type": "Universal notation"
+          },
+          "script-x": {
+            "meaning": "This is a symbol we’ve chosen to represent our dataset.",
+            "say": "Script X",
+            "type": "Locally defined variable"
+          }
+        }
+      },
+      "source": [
+        "## 手法\n",
+        "\n",
+        "それぞれが $N$ 個の [特徴](gloss:features) を持つ$M$個のサンプルで構成される古典的なデータセット$\\mathscr{X}$を考えてみましょう: $$\\class{script-x}{\\mathscr{X}} = \\class{brace}{{}x^{(1)},\\class{ellipsis}{\\dots},\\cssId{_x-lil-m}{x^{(m)}},\\dots,x^{(M)}\\class{brace}{}}$$ ここで、$x^{(m)}$は$m = 1, ..., M$の$N$  次元ベクトルです。このデータセットを量子ビットのシステムで表すために、さまざまな埋め込み手法を使用できます。以下に、その一部を参考文献[1](#References)、 [2](#References)に従って簡単に説明し、実装します。"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 計算基底符号化\n",
+        "\n",
+        "計算基底符号化は、古典的な$N$ビット文字列を$N$量子ビットシステムの [計算基底状態](gloss:computational-basis-state) に関連付けます。 たとえば、$x = 5$の場合、これは$0101$として$4$ビット文字列として表すことができ、量子状態$|0101\\rangle$として4量子ビットシステムによって表すことができます。より一般的には、$N$ビット文字列：$x = (b_1, b_2, ... , b_N)$の場合、対応する$N$-量子ビット状態は$\\cssId{ket-x}{| x \\rangle} = | b_1, b_2, ... , b_N \\rangle$です。ここで、$n = 1 , \\dots , N$に対して$b_n \\class{in}{\\in} {0,1}$ です。\n",
+        "\n",
+        "上記の古典的なデータセット$\\mathscr{X}$の場合に、計算基底符号化を使用するには、各データポイントを$N$ビット文字列$x^{(m)} = (b_1, b_2, ... , b_N)$ とし、これを量子状態 $|x^{m}\\rangle = |b_1, b_2, ... , b_N \\rangle$ に直接マッピングします。ここで$n = 1, ...,  N$ において、$b_n \\in {0, 1 } $であり、また、$m = 1, ..., M$です。 データセット全体を計算基底状態の重ね合わせとして表すことができます。\n",
+        "\n",
+        "$$\\cssId{_ket-dataset}{| \\mathscr{X} \\rangle} = \\frac{1}{\\sqrt{\\cssId{_m}{M}}}\\cssId{*sum-m}{\\sum*{m=1}^{M}|x^{m} \\rangle} $$\n",
+        "\n",
+        "<!-- ::: q-block -->\n",
+        "\n",
+        "### 計算基底符号化\n",
+        "\n",
+        "```\n",
+        "q-statevector-binary-encoding\n",
+        "  p 左の入力データセットにビット列を追加したり削除したりすると、右の状態ベクトルに計算基底符号化がどのように符号化されるかを見ることができる。\n",
+        "```\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "Qiskitでは、どのような状態でデータセットを符号化するかを計算したら、`initialize` 関数を使用して準備することができます。 たとえば、データセット $\\mathscr{X} = {x^{(1)}=101, x^{(2)}=111}$ は、$|\\mathscr{X}\\rangle= \\frac{1}{\\sqrt{2}}(|101\\rangle+|111\\rangle)$ の状態としてエンコードされます："
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 1,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "image/svg+xml": [
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+            ],
+            "text/plain": [
+              "<Figure size 808.997x204.68 with 1 Axes>"
+            ]
+          },
+          "execution_count": 1,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "import math\n",
+        "from qiskit import QuantumCircuit\n",
+        "\n",
+        "desired_state = [\n",
+        "    0,\n",
+        "    0,\n",
+        "    0,\n",
+        "    0,\n",
+        "    0,\n",
+        "    1 / math.sqrt(2),\n",
+        "    0,\n",
+        "    1 / math.sqrt(2)]\n",
+        "\n",
+        "qc = QuantumCircuit(3)\n",
+        "qc.initialize(desired_state, [0,1,2])\n",
+        "\n",
+        "qc.decompose().decompose().decompose().decompose().decompose().draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "この例は、計算基底符号化の欠点も示しています。つまり、計算基底符号化は理解するのは簡単ですが、状態ベクトルは非常に疎になる可能性があり、実装するスキームが通常効率的ではありません。 "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "formulas": {
+          "_a-norm": {
+            "meaning": "This is a normalization constant. We can calculate it from the inverse of the Euclidean (l2) norm of the datapoint vector.",
+            "say": "A norm"
+          }
+        }
+      },
+      "source": [
+        "### 振幅符号化\n",
+        "\n",
+        "Amplitude encoding encodes data into the amplitudes of a quantum state. It represents a normalised classical $N$-dimensional datapoint, $x$, as the amplitudes of a $n$-qubit quantum state, $|\\psi_x\\rangle$: $$|\\psi_x\\rangle = \\sum_{i=1}^N x_i |i\\rangle$$ where $N = 2^n$, $x_i$ is the $i^{th}$ element of $x$ and $|i\\rangle$ is the $i^{th}$ computational basis state.\n",
+        "\n",
+        "上記の古典的なデータセット$\\mathscr{X}$ を符号化するために、すべての$M$ $N$次元データポイントを長さ $N \\times M$ の1つの振幅ベクトルに連結します: $$\\alpha=\\cssId{*a-norm}{A*{\\text{norm}}}(x_{1}^{(1)},...,x_{N}^{(1)},...,x_{1}^{(m)},...,x_{N}^{(m)},...,x_{1}^{(M)},...,x_{N}^{(M)})$$  ここで、$A_{\\text{norm}}$ は正規化定数であり、$|\\alpha|^2 = 1$ です。 データセット$\\mathscr{X}$ は、計算基底で次のように表すことができます。 $$|\\mathscr{X}\\rangle = \\sum_{i=1}^N \\alpha_i |i\\rangle$$  ここで、$\\alpha_i$は振幅ベクトルの要素であり、$|i\\rangle$は計算基底状態です。 符号化される振幅の数は$N \\times M$です。 $n$量子ビットのシステムは$2^n$個の振幅を提供するので、振幅の埋め込みには$n \\ge \\mathrm{log}_2(NM)$個の量子ビットが必要です。\n",
+        "\n",
+        "<!-- ::: q-block -->\n",
+        "\n",
+        "### 振幅符号化\n",
+        "\n",
+        "```\n",
+        "q-statevector-amplitude-encoding\n",
+        "  p 左側のデータポイントの値を変更し、振幅エンコーディングがこれらを右側の状態ベクトルとしてどのようにエンコードするかを確認します。\n",
+        "```\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "例として、振幅符号化を使用してデータセット$\\mathscr{X}= {x^{(1)}=(1.5,0), x^{(2)}=(-2,3)}$ を符号化してみましょう。両方のデータポイントを連結し、結果のベクトルを正規化すると、次のようになります: $$\\alpha = \\frac{1}{\\sqrt{15.25}}(1.5,0,-2,3)$$ 結果として得られる2量子ビットの量子状態は次のようになります: $$|\\mathscr{X}\\rangle = \\frac{1}{\\sqrt{15.25}}(1.5|00\\rangle-2|10\\rangle+3|11\\rangle)$$\n",
+        "\n",
+        "In the example above, the total number of elements of the amplitude vector, $N \\times M$, is a power of 2. When $N \\times M$ is not a power of 2, we can simply choose a value for $n$ such that $2^n\\geq MN$ and pad the amplitude vector with uninformative constants.\n",
+        "\n",
+        " 計算基底符号化と同様に、データセットを符号化する状態を計算したら、Qiskitで`initialize`関数を使用してを準備できます:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 7,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 688.452x144.48 with 1 Axes>"
+            ]
+          },
+          "execution_count": 7,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "desired_state = [\n",
+        "    1 / math.sqrt(15.25) * 1.5,\n",
+        "    0,\n",
+        "    1 / math.sqrt(15.25) * -2,\n",
+        "    1 / math.sqrt(15.25) * 3]\n",
+        "\n",
+        "qc = QuantumCircuit(2)\n",
+        "qc.initialize(desired_state, [0,1])\n",
+        "\n",
+        "qc.decompose().decompose().decompose().decompose().decompose().draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "振幅符号化の利点は、符号化に必要なのは$\\mathrm{log}_2(NM)$量子ビットのみであるということです。 ただし、その後のアルゴリズムは量子状態の振幅を操作する必要があり、量子状態を準備し測定する方法は効率的ではない傾向があります。 "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "formulas": {
+          "_big-o-times-n": {
+            "meaning": "This represents the tensor product operation over N qubits.",
+            "say": "big o-times"
+          },
+          "_big-o-times-n2": {
+            "meaning": "This represents the tensor product operation over N/2 qubits.",
+            "say": "big o-times"
+          }
+        }
+      },
+      "source": [
+        "### 角度符号化\n",
+        "\n",
+        "Angle encoding encodes $N$ features into the rotation angles of $n$ qubits, where $N \\le n$. For example, the datapoint $x = (x_1,...,x_N)$ can be encoded as: $$\\cssId{_}{|x\\rangle} = \\class{*big-o-times-n}{\\bigotimes^N*{i=1}} \\cos(x_i)|0\\rangle + \\sin(x_i)|1\\rangle$$\n",
+        "\n",
+        "これは、前の2つの符号化方法とは異なり、データセット全体ではなく、一度に1つのデータポイントのみを符号化する方法です。ただし、使用するのは$N$量子ビットで量子回路の深さも一定であるため、現在の量子ハードウェアに適用可能です。\n",
+        "\n",
+        "角度符号化は[ユニタリー演算](gloss:unitary)で指定することができます：$$ S_{x_j} = \\class{*big-o-times-n}{\\bigotimes*{i=1}^N} U(x_j^{(i)}) $$\n",
+        "\n",
+        "ここで\n",
+        "\n",
+        "$$ U(x_j^{(i)}) = \\begin{bmatrix} \\cos(x_j^{(i)}) &amp; -\\sin(x_j^{(i)}) \\ \\sin(x_j^{(i)}) &amp; \\cos(x_j^{(i)}) \\ \\end{bmatrix} $$\n",
+        "\n",
+        "$Y$軸周りの単一量子ビットの回転は次のとおりでした:  $$RY(\\theta) = \\exp(-i \\frac{\\theta}{2} Y) = \\begin{pmatrix} \\cos{\\frac{\\theta}{2}} &amp; -\\sin{\\frac{\\theta}{2}} \\ \\sin{\\frac{\\theta}{2}} &amp; \\cos{\\frac{\\theta}{2}} \\end{pmatrix} $$\n",
+        "\n",
+        " $U(x_j^{(i)}) = RY(2x_j^{(i)})$に注意し、例として、qiskitを使用してデータポイント$x = (0, \\pi/4, \\pi/2)$ を符号化します："
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 8,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 146.797x204.68 with 1 Axes>"
+            ]
+          },
+          "execution_count": 8,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "qc = QuantumCircuit(3)\n",
+        "\n",
+        "qc.ry(0, 0)\n",
+        "qc.ry(math.pi/4, 1)\n",
+        "qc.ry(math.pi/2, 2)\n",
+        "qc.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "高密度角度符号化は、角度符号化を少し一般化したものであり、相対位相を使用して1量子ビットごとに2つの特徴を符号化します。データポイント$x = (x_1,...,x_N)$は次のように符号化されます: $$|x\\rangle = \\class{*big-o-times-n2}{\\bigotimes*{i=1}^{N/2}} \\cos(x_{2i-1})|0\\rangle + e^{i x_{2i}}\\sin(x_{2i-1})|1\\rangle$$\n",
+        "\n",
+        "Although the angle and dense angle encoding use sinuosoids and exponentials, there is nothing special about these functions, and we can easily abstract these to a general class of qubit encodings that use arbitrary functions, or define the encodings as arbitrary unitaries, implemented as parameterized quantum circuits."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 任意の符号化\n",
+        "\n",
+        "任意の符号化は、$N$個の特徴を$n$量子ビット上の$N$個のパラメーター化されたゲートの回転として符号化します。ここで、$n \\leq N$です。角度符号化と同様に、データセット全体ではなく、一度に1つのデータポイントのみを符号化します。 また、一定の深さの量子回路と$n \\leq N$ 量子ビットを使用しているため、現在の量子ハードウェアで実行できます。 "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "たとえば、[`EfficientSU2`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.EfficientSU2.html)回路を使用して12個の特徴を符号化するには、3個の量子ビットを使用するだけです:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 4,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 628.397x204.68 with 1 Axes>"
+            ]
+          },
+          "execution_count": 4,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "from qiskit.circuit.library import EfficientSU2\n",
+        "\n",
+        "circuit = EfficientSU2(num_qubits=3, reps=1, insert_barriers=True)\n",
+        "circuit.decompose().draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "例えば、データポイント$x = [0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2]$ を12の特徴で符号化し、パラメーター化された各ゲートを使用して異なる特徴を符号化します。"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 5,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "image/svg+xml": [
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+            ],
+            "text/plain": [
+              "<Figure size 1049.8x204.68 with 1 Axes>"
+            ]
+          },
+          "execution_count": 5,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "x = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 1.1, 1.2]\n",
+        "\n",
+        "encode = circuit.bind_parameters(x)\n",
+        "encode.decompose().draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_z4XzacisEy"
+      },
+      "source": [
+        "The Qiskit [`ZZFeatureMap`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ZZFeatureMap.html) circuit with 3 qubits, only encodes a datapoint of 3 features, despite having 6 parameterized gates:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 6,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 1170.2x204.68 with 1 Axes>"
+            ]
+          },
+          "execution_count": 6,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "from qiskit.circuit.library import ZZFeatureMap\n",
+        "\n",
+        "circuit = ZZFeatureMap(3, reps=1, insert_barriers=True)\n",
+        "circuit.decompose().draw()"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 7,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "image/svg+xml": [
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+            ],
+            "text/plain": [
+              "<Figure size 1110x204.68 with 1 Axes>"
+            ]
+          },
+          "execution_count": 7,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "x = [0.1, 0.2, 0.3]\n",
+        "\n",
+        "encode = circuit.bind_parameters(x)\n",
+        "encode.decompose().draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### Quick quiz\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"qml-encoding-0\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\n",
+        "パラメーター化された量子回路には16個のパラメーターがあります。 エンコードできる機能の最大数はいくつですか？\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. 4\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. 8\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option(correct) -->\n",
+        "\n",
+        "1. 16\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: .option -->\n",
+        "\n",
+        "1. 32\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->\n",
+        "\n",
+        "<!-- ::: -->"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "formulas": {
+          "big-o-times": {
+            "meaning": "In the same way a big sigma (Σ) represents summation over different values, this big 'otimes' means we take the Kronecker product of the formula to it's right for a set of values.",
+            "say": "big o-times"
+          }
+        }
+      },
+      "source": [
+        "The performance of different parameterized quantum circuits on different types of data is an active area of investigation.\n",
+        "\n",
+        "<div style=\"display: none\"> $$\\cssId{big-o-times}{\\bigotimes}$$</div>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 参考文献\n",
+        "\n",
+        "1. Maria Schuld and Francesco Petruccione, *Supervised Learning with Quantum Computers*, Springer 2018, [doi:10.1007/978-3-319-96424-9](https://www.springer.com/gp/book/9783319964232).\n",
+        "2. Ryan LaRose and Brian Coyle, *Robust data encodings for quantum classifiers*, Physical Review A 102, 032420 (2020), [doi:10.1103/PhysRevA.102.032420](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.102.032420), [arXiv:2003.01695](https://arxiv.org/abs/2003.01695)."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 8,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "name": "stderr",
+          "output_type": "stream",
+          "text": [
+            "/usr/local/anaconda3/lib/python3.7/site-packages/qiskit/aqua/__init__.py:86: DeprecationWarning: The package qiskit.aqua is deprecated. It was moved/refactored to qiskit-terra For more information see <https://github.com/Qiskit/qiskit-aqua/blob/main/README.md#migration-guide>\n",
+            "  warn_package('aqua', 'qiskit-terra')\n"
+          ]
+        },
+        {
+          "data": {
+            "text/html": [
+              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.18.3</td></tr><tr><td><code>qiskit-aer</code></td><td>0.9.0</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.6.0</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.16.0</td></tr><tr><td><code>qiskit-aqua</code></td><td>0.9.5</td></tr><tr><td><code>qiskit</code></td><td>0.30.1</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.7.7 (default, May  6 2020, 04:59:01) \n",
+              "[Clang 4.0.1 (tags/RELEASE_401/final)]</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>32.0</td></tr><tr><td colspan='2'>Thu Nov 11 16:58:07 2021 GMT</td></tr></table>"
+            ],
+            "text/plain": [
+              "<IPython.core.display.HTML object>"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "import qiskit.tools.jupyter\n",
+        "%qiskit_version_table"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 4
+}

From e4908b2f611cd4ed971b8ca28d3754b840db1f16 Mon Sep 17 00:00:00 2001
From: Daiki Murata <d.murata0623@gmail.com>
Date: Tue, 14 Jun 2022 04:21:30 +0000
Subject: [PATCH 52/62] Translate encoding.ipynb via GitLocalize

---
 .../ja/quantum-machine-learning/encoding.ipynb    | 15 +++++++--------
 1 file changed, 7 insertions(+), 8 deletions(-)

diff --git a/translations/ja/quantum-machine-learning/encoding.ipynb b/translations/ja/quantum-machine-learning/encoding.ipynb
index 33248f127..a68cc0be1 100644
--- a/translations/ja/quantum-machine-learning/encoding.ipynb
+++ b/translations/ja/quantum-machine-learning/encoding.ipynb
@@ -178,7 +178,7 @@
       "source": [
         "### 振幅符号化\n",
         "\n",
-        "Amplitude encoding encodes data into the amplitudes of a quantum state. It represents a normalised classical $N$-dimensional datapoint, $x$, as the amplitudes of a $n$-qubit quantum state, $|\\psi_x\\rangle$: $$|\\psi_x\\rangle = \\sum_{i=1}^N x_i |i\\rangle$$ where $N = 2^n$, $x_i$ is the $i^{th}$ element of $x$ and $|i\\rangle$ is the $i^{th}$ computational basis state.\n",
+        "振幅符号化は、データを量子状態の振幅に符号化します。これは、正規化された古典的な$N$次元データポイント$x$を、$n$量子ビットの量子状態$|\\psi_x\\rangle$の振幅として表します：$$|\\psi_x\\rangle = \\sum_{i=1}^N x_i |i\\rangle$$ where $N = 2^n$  ここで、$N = 2^n$、$x_i$ は $x$ の $i^{th}$ 番目の要素であり、$|i\\rangle$ は $i^{th}$ 番目の計算基底状態です。\n",
         "\n",
         "上記の古典的なデータセット$\\mathscr{X}$ を符号化するために、すべての$M$ $N$次元データポイントを長さ $N \\times M$ の1つの振幅ベクトルに連結します: $$\\alpha=\\cssId{*a-norm}{A*{\\text{norm}}}(x_{1}^{(1)},...,x_{N}^{(1)},...,x_{1}^{(m)},...,x_{N}^{(m)},...,x_{1}^{(M)},...,x_{N}^{(M)})$$  ここで、$A_{\\text{norm}}$ は正規化定数であり、$|\\alpha|^2 = 1$ です。 データセット$\\mathscr{X}$ は、計算基底で次のように表すことができます。 $$|\\mathscr{X}\\rangle = \\sum_{i=1}^N \\alpha_i |i\\rangle$$  ここで、$\\alpha_i$は振幅ベクトルの要素であり、$|i\\rangle$は計算基底状態です。 符号化される振幅の数は$N \\times M$です。 $n$量子ビットのシステムは$2^n$個の振幅を提供するので、振幅の埋め込みには$n \\ge \\mathrm{log}_2(NM)$個の量子ビットが必要です。\n",
         "\n",
@@ -195,7 +195,7 @@
         "\n",
         "例として、振幅符号化を使用してデータセット$\\mathscr{X}= {x^{(1)}=(1.5,0), x^{(2)}=(-2,3)}$ を符号化してみましょう。両方のデータポイントを連結し、結果のベクトルを正規化すると、次のようになります: $$\\alpha = \\frac{1}{\\sqrt{15.25}}(1.5,0,-2,3)$$ 結果として得られる2量子ビットの量子状態は次のようになります: $$|\\mathscr{X}\\rangle = \\frac{1}{\\sqrt{15.25}}(1.5|00\\rangle-2|10\\rangle+3|11\\rangle)$$\n",
         "\n",
-        "In the example above, the total number of elements of the amplitude vector, $N \\times M$, is a power of 2. When $N \\times M$ is not a power of 2, we can simply choose a value for $n$ such that $2^n\\geq MN$ and pad the amplitude vector with uninformative constants.\n",
+        "上記の例では、振幅ベクトルの要素の総数$N \\times M$は2の累乗です。$N \\times M$が2の累乗でない場合、$2^n\\geq MN$ となるように$n$の値を選び、振幅ベクトルに無意味な定数を埋め込めばよいです。\n",
         "\n",
         " 計算基底符号化と同様に、データセットを符号化する状態を計算したら、Qiskitで`initialize`関数を使用してを準備できます:"
       ]
@@ -259,7 +259,7 @@
       "source": [
         "### 角度符号化\n",
         "\n",
-        "Angle encoding encodes $N$ features into the rotation angles of $n$ qubits, where $N \\le n$. For example, the datapoint $x = (x_1,...,x_N)$ can be encoded as: $$\\cssId{_}{|x\\rangle} = \\class{*big-o-times-n}{\\bigotimes^N*{i=1}} \\cos(x_i)|0\\rangle + \\sin(x_i)|1\\rangle$$\n",
+        "角度符号化は、$N$ 個の特徴(feature)を $n$量子ビットの回転角に符号化します。ここで、$N \\le n$です。 たとえば、データポイント$x = (x_1,...,x_N)$ は次のように符号化できます。$$\\cssId{_}{|x\\rangle} = \\class{*big-o-times-n}{\\bigotimes^N*{i=1}} \\cos(x_i)|0\\rangle + \\sin(x_i)|1\\rangle$$\n",
         "\n",
         "これは、前の2つの符号化方法とは異なり、データセット全体ではなく、一度に1つのデータポイントのみを符号化する方法です。ただし、使用するのは$N$量子ビットで量子回路の深さも一定であるため、現在の量子ハードウェアに適用可能です。\n",
         "\n",
@@ -311,7 +311,7 @@
       "source": [
         "高密度角度符号化は、角度符号化を少し一般化したものであり、相対位相を使用して1量子ビットごとに2つの特徴を符号化します。データポイント$x = (x_1,...,x_N)$は次のように符号化されます: $$|x\\rangle = \\class{*big-o-times-n2}{\\bigotimes*{i=1}^{N/2}} \\cos(x_{2i-1})|0\\rangle + e^{i x_{2i}}\\sin(x_{2i-1})|1\\rangle$$\n",
         "\n",
-        "Although the angle and dense angle encoding use sinuosoids and exponentials, there is nothing special about these functions, and we can easily abstract these to a general class of qubit encodings that use arbitrary functions, or define the encodings as arbitrary unitaries, implemented as parameterized quantum circuits."
+        "角度および高密度角度符号化は、正弦波関数および指数関数を使用しますが、この関数は特別である必要はなく、任意の関数を使う一般的な量子ビットの符号化クラスに簡単に抽象化できます。次のように、任意のユニタリー演算で定義されたパラメーター化された量子回路で符号化を実装することもできます。"
       ]
     },
     {
@@ -399,10 +399,9 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_z4XzacisEy"
       },
       "source": [
-        "The Qiskit [`ZZFeatureMap`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ZZFeatureMap.html) circuit with 3 qubits, only encodes a datapoint of 3 features, despite having 6 parameterized gates:"
+        "3量子ビットのQiskit[`ZZFeatureMap`](https://qiskit.org/documentation/stubs/qiskit.circuit.library.ZZFeatureMap.html)  回路は、6つのパラメーター化されたゲートがあるにもかかわらず、3つの機能のデータポイントしか符号化しません:"
       ]
     },
     {
@@ -468,7 +467,7 @@
       "source": [
         "<!-- ::: q-block.exercise -->\n",
         "\n",
-        "### Quick quiz\n",
+        "### クイッククイズ\n",
         "\n",
         "<!-- ::: q-quiz(goal=\"qml-encoding-0\") -->\n",
         "\n",
@@ -518,7 +517,7 @@
         }
       },
       "source": [
-        "The performance of different parameterized quantum circuits on different types of data is an active area of investigation.\n",
+        "さまざまなタイプのデータに対するさまざまなパラメータ化された量子回路の性能は、活発に研究されている分野です。\n",
         "\n",
         "<div style=\"display: none\"> $$\\cssId{big-o-times}{\\bigotimes}$$</div>"
       ]

From 123bd68e86db5734797bc458b5ca3ccf48252e8b Mon Sep 17 00:00:00 2001
From: "Marco A. Nava Aguilar" <herestkamah@gmail.com>
Date: Tue, 14 Jun 2022 05:05:03 +0000
Subject: [PATCH 53/62] Translate deutsch-jozsa.ipynb via GitLocalize

---
 .../es/ch-algorithms/deutsch-jozsa.ipynb      | 1118 +++++++++++++++++
 1 file changed, 1118 insertions(+)
 create mode 100644 translations/es/ch-algorithms/deutsch-jozsa.ipynb

diff --git a/translations/es/ch-algorithms/deutsch-jozsa.ipynb b/translations/es/ch-algorithms/deutsch-jozsa.ipynb
new file mode 100644
index 000000000..e61f80feb
--- /dev/null
+++ b/translations/es/ch-algorithms/deutsch-jozsa.ipynb
@@ -0,0 +1,1118 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "tags": [
+          "remove_cell"
+        ]
+      },
+      "source": [
+        "# Algoritmo de Deutsch-Jozsa"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "En esta sección, primero presentamos el problema de Deutsch-Jozsa y los algoritmos clásicos y cuánticos para resolverlo. Luego implementamos el algoritmo cuántico usando Qiskit y lo ejecutamos en un simulador y en un dispositivo."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_uAozTzR78t"
+      },
+      "source": [
+        "## 1. Introduction <a id='introduction'></a>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "El algoritmo Deutsch-Jozsa, presentado por primera vez en la referencia [1], fue el primer ejemplo de un algoritmo cuántico que funciona mejor que el mejor algoritmo clásico. Demostró que puede haber ventajas en el uso de una computadora cuántica como herramienta computacional para un problema específico."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 1.1 Deutsch-Jozsa Problem <a id=\"djproblem\"> </a>\n",
+        "\n",
+        "Tenemos una función booleana oculta $f$, que toma como entrada una cadena de bits y devuelve $0$ o $1$, es decir:\n",
+        "\n",
+        "$$ f({x_0,x_1,x_2,...}) \\rightarrow 0 \\textrm{ o } 1 \\textrm{ , donde } x_n \\textrm{ es } 0 \\textrm{ o } 1$$\n",
+        "\n",
+        "La propiedad de la función booleana dada es que se garantiza que sea balanceada o constante. Una función constante devuelve todos los $0$ o todos los $1$ para cualquier entrada, mientras que una función balanceada devuelve $0$ para exactamente la mitad de todas las entradas y $1$ para la otra mitad. Nuestra tarea es determinar si la función dada es balanceada o constante.\n",
+        "\n",
+        "Ten en cuenta que el problema de Deutsch-Jozsa es una extensión de $n$ bits del problema de Deutsch de un solo bit.\n",
+        "\n",
+        "### 1.2 The Classical Solution <a id=\"classical-solution\"> </a>\n",
+        "\n",
+        "Clásicamente, en el mejor de los casos, dos consultas al oráculo pueden determinar si la función booleana oculta, $f(x)$, es balanceada: por ejemplo, si obtenemos ambas $f(0,0,0,...)\\rightarrow 0$ y $f(1,0,0,...) \\rightarrow 1$, entonces sabemos que la función está balanceada, ya que hemos obtenido las dos salidas diferentes.\n",
+        "\n",
+        "En el peor de los casos, si continuamos viendo la misma salida para cada entrada que intentamos, tendremos que verificar exactamente la mitad de todas las entradas posibles más una para estar seguros de que $f(x)$ es constante. Dado que el número total de entradas posibles es $2^n$, esto implica que necesitamos $2^{n-1}+1$ entradas de prueba para estar seguros de que $f(x)$ es constante en el peor de los casos. Por ejemplo, para una cadena de bits de $4$, si verificamos $8$ de las $16$ combinaciones posibles, obteniendo todos los $0$, aún es posible que la entrada $9^\\textrm{a}$ devuelva $1$ y $f(x)$ está balanceada. Probabilísticamente, este es un evento muy improbable. De hecho, si obtenemos el mismo resultado continuamente en sucesión, podemos expresar la probabilidad de que la función sea constante en función de $k$ entradas como:\n",
+        "\n",
+        "$$ P_\\textrm{constant}(k) = 1 - \\frac{1}{2^{k-1}} \\qquad \\textrm{para } 1 &lt; k \\leq 2^{n-1}$$\n",
+        "\n",
+        "Realistically, we could opt to truncate our classical algorithm early, say if we were over x% confident. But if we want to be 100% confident, we would need to check $2^{n-1}+1$ inputs."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 1.3 Quantum Solution <a id=\"quantum-solution\"> </a>\n",
+        "\n",
+        "Using a quantum computer, we can solve this problem with 100% confidence after only one call to the function $f(x)$, provided we have the function $f$ implemented as a quantum oracle, which maps the state $\\vert x\\rangle \\vert y\\rangle $ to $ \\vert x\\rangle \\vert y \\oplus f(x)\\rangle$, where $\\oplus$ is addition modulo $2$. Below is the generic circuit for the Deutsch-Jozsa algorithm.\n",
+        "\n",
+        "![imagen1](images/deutsch_steps.png)\n",
+        "\n",
+        "Ahora, repasemos los pasos del algoritmo:\n",
+        "\n",
+        "<ol>\n",
+        "   <li>Prepara dos registros cuánticos. El primero es un registro de $n$ qubits inicializado en $|0\\rangle$, y el segundo es un registro de un qubit inicializado en $|1\\rangle$:</li>\n",
+        "</ol>\n",
+        "\n",
+        "$$\\vert \\psi_0 \\rangle = \\vert0\\rangle^{\\otimes n} \\vert 1\\rangle$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>         Apply a Hadamard gate to each qubit: </li>\n",
+        "\n",
+        "\n",
+        "$$\\vert \\psi_1 \\rangle = \\frac{1}{\\sqrt{2^{n+1}}}\\sum_{x=0}^{2^n-1} \\vert x\\rangle \\left(|0\\rangle - |1 \\rangle \\right)$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>Aplica el oráculo cuántico $\\vert x\\rangle \\vert y\\rangle$ a $\\vert x\\rangle \\vert y \\oplus f(x)\\rangle$: $$ \\begin{aligned} \\lvert \\psi_2 \\rangle &amp; = \\frac{1}{\\sqrt{2^{n+1}}}\\sum_{x=0}^{2^n-1} \\vert x\\rangle (\\vert f(x)\\rangle - \\vert 1 \\oplus f(x)\\rangle) \\\\ &amp; = \\frac{1}{\\sqrt{2^{n+1}}}\\sum_{x=0}^{2^n-1}(-1)^{f(x)}|x\\rangle ( |0\\rangle - |1\\rangle ) \\end{aligned} $$</li>\n",
+        "\n",
+        "\n",
+        "ya que para cada $x,f(x)$ es $0$ o $1$.\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>        At this point the second single qubit register may be ignored. Apply a Hadamard gate to each qubit in the first register:         $$         \\begin{aligned}             \\lvert \\psi_3 \\rangle                  &amp; = \\frac{1}{2^n}\\sum_{x=0}^{2^n-1}(-1)^{f(x)}                     \\left[ \\sum_{y=0}^{2^n-1}(-1)^{x \\cdot y}                      \\vert y \\rangle \\right] \\\\                 &amp; = \\frac{1}{2^n}\\sum_{y=0}^{2^n-1}                     \\left[ \\sum_{x=0}^{2^n-1}(-1)^{f(x)}(-1)^{x \\cdot y} \\right]                     \\vert y \\rangle         \\end{aligned}         $$ </li>\n",
+        "\n",
+        "\n",
+        "donde $x \\cdot y = x_0y_0 \\oplus x_1y_1 \\oplus \\ldots \\oplus x_{n-1}y_{n-1}$ es la suma del producto bit a bit.\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>Medir el primer registro. Observa que la probabilidad de medir $\\vert 0 \\rangle ^{\\otimes n} = \\lvert \\frac{1}{2^n}\\sum_{x=0}^{2^n-1}(-1) ^{f(x)} \\rvert^2$, que se evalúa como $1$ si $f(x)$ es constante y $0$ si $f(x)$ es balanceada.</li>\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "### 1.4 Why Does This Work? <a id=\"why-does-this-work\"> </a>\n",
+        "\n",
+        "- **    Oráculo Constante**\n",
+        "\n",
+        "When the oracle is *constant*, it has no effect (up to a global phase) on the input qubits, and the quantum states before and after querying the oracle are the same. Since the H-gate is its own inverse, in Step 4 we reverse Step 2 to obtain the initial quantum state of $|00\\dots 0\\rangle$ in the first register.\n",
+        "\n",
+        "# $$ H^{\\otimes n}\\begin{bmatrix} 1 \\ 0 \\ 0 \\ \\vdots \\ 0 \\end{bmatrix}\n",
+        "\n",
+        "# \\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix} \\quad \\xrightarrow{\\text{after } U_f} \\quad H^{\\otimes n}\\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix}\n",
+        "\n",
+        "\\begin{bmatrix} 1 \\ 0 \\ 0 \\ \\vdots \\ 0 \\end{bmatrix} $$\n",
+        "\n",
+        "- **Balanced Oracle**\n",
+        "\n",
+        "After step 2, our input register is an equal superposition of all the states in the computational basis. When the oracle is *balanced*, phase kickback adds a negative phase to exactly half these states:\n",
+        "\n",
+        "# $$ U_f \\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix}\n",
+        "\n",
+        "\\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} -1 \\ 1 \\ -1 \\ \\vdots \\ 1 \\end{bmatrix} $$\n",
+        "\n",
+        "El estado cuántico después de consultar el oráculo es ortogonal al estado cuántico antes de consultar el oráculo. Por lo tanto, en el Paso 4, al aplicar las compuertas H, debemos terminar con un estado cuántico que sea ortogonal a $|00\\dots 0\\rangle$. Esto significa que nunca debemos medir el estado cero.\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 2. Worked Example  <a id=\"example\"></a>\n",
+        "\n",
+        "Veamos un ejemplo específico para una función balanceada de dos bits:\n",
+        "\n",
+        "Consider a two-bit function $f(x_0,x_1)=x_0 \\oplus x_1$ such that\n",
+        "\n",
+        "$f(0,0)=0$\n",
+        "\n",
+        "$f(0,1)=1$\n",
+        "\n",
+        "$f(1,0)=1$\n",
+        "\n",
+        "$f(1,1)=0$\n",
+        "\n",
+        "El oráculo de fase correspondiente de este oráculo de dos bits es $U_f \\lvert x_1, x_0 \\rangle = (-1)^{f(x_1, x_0)}\\lvert x \\rangle$\n",
+        "\n",
+        "Ahora comprobaremos si este oráculo funciona como se esperaba tomando un estado de ejemplo $$\\lvert \\psi_0 \\rangle = \\lvert 0 0 \\rangle_{01} \\otimes \\lvert 1 \\rangle_{2} $$\n",
+        "\n",
+        "<ol>\n",
+        "    <li>El primer registro de dos qubits se inicializa en $|00\\rangle$ y el segundo registro qubit en $|1\\rangle$</li>\n",
+        "</ol>\n",
+        "\n",
+        "(Nota que estamos usando los subíndices 0, 1 y 2 para indizar los qubits. Un subíndice de \"01\" indica el estado del registro que contiene los qubits 0 y 1)\n",
+        "\n",
+        "$$\\lvert \\psi_0 \\rangle = \\lvert 0 0 \\rangle_{01} \\otimes \\lvert 1 \\rangle_{2} $$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>Aplicar Hadamard en todos los qubits</li>\n",
+        "\n",
+        "\n",
+        "$$\\lvert \\psi_1 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle + \\lvert 0 1 \\rangle + \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)*{01} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)*{2}  $$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li> The oracle function can be implemented as $\\text{Q}_f = CX_{02}CX_{12}$,            $$        \\begin{aligned}             \\lvert \\psi_2 \\rangle =  \\frac{1}{2\\sqrt{2}} \\left[ \\lvert 0 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 0 \\oplus 0 \\rangle - \\lvert 1 \\oplus 0 \\oplus 0 \\rangle \\right)_{2} \\\\                   + \\lvert 0 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 0 \\oplus 1 \\rangle - \\lvert 1 \\oplus 0 \\oplus 1 \\rangle \\right)_{2} \\\\                   + \\lvert 1 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 1 \\oplus 0 \\rangle - \\lvert 1 \\oplus 1 \\oplus 0 \\rangle \\right)_{2} \\\\                   + \\lvert 1 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 1 \\oplus 1 \\rangle - \\lvert 1 \\oplus 1 \\oplus 1 \\rangle \\right)_{2} \\right]         \\end{aligned}          $$    </li>\n",
+        "\n",
+        "\n",
+        "   <li>Simplifying this, we get the following:         $$        \\begin{aligned}         \\lvert \\psi_2 \\rangle &amp; = \\frac{1}{2\\sqrt{2}} \\left[ \\lvert 0 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} - \\lvert 0 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert  1 \\rangle \\right)_{2} - \\lvert 1 0 \\rangle_{01} \\otimes \\left( \\lvert 0  \\rangle - \\lvert 1 \\rangle \\right)_{2} + \\lvert 1 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2}  \\right] \\\\         &amp; = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle - \\lvert 0 1 \\rangle - \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)_{01} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} \\\\         &amp; = \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{0} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{1} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2}         \\end{aligned}         $$    </li>\n",
+        "\n",
+        "\n",
+        "   <li>Aplicar Hadamard en el primer registro</li>\n",
+        "\n",
+        "\n",
+        "$$ \\lvert \\psi_3\\rangle = \\lvert 1 \\rangle_{0} \\otimes \\lvert 1 \\rangle_{1} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} $$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>La medición de los primeros dos qubits dará $11$ distintos de cero, lo que indica una función balanceada.</li>\n",
+        "\n",
+        "\n",
+        "\n",
+        "Puedes probar ejemplos similares usando el widget a continuación. Presiona los botones para agregar compuertas H y oráculos, vuelve a ejecutar la celda y/o configura `case=\"constant\"` para probar diferentes oráculos."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "scrolled": true
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "from qiskit_textbook.widgets import dj_widget\n",
+        "dj_widget(size=\"small\", case=\"balanced\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 3. Creating Quantum Oracles <a id=\"creating-quantum-oracles\"> </a>\n",
+        "\n",
+        "Veamos algunas formas diferentes en que podemos crear un oráculo cuántico.\n",
+        "\n",
+        "Para una función constante, es simple:\n",
+        "\n",
+        "$\\qquad$ 1. if f(x) = 0, then apply the $I$ gate to the qubit in register 2.\n",
+        " $\\qquad$ 2. if f(x) = 1, then apply the $X$ gate to the qubit in register 2.\n",
+        "\n",
+        "Para una función balanceada, hay muchos circuitos diferentes que podemos crear. Una de las formas en que podemos garantizar que nuestro circuito esté balanceado es realizando un CNOT para cada qubit en el registro 1, con el qubit en el registro 2 como objetivo. Por ejemplo:\n",
+        "\n",
+        "![imagen2](images/deutsch_balanced1.svg)\n",
+        "\n",
+        "En la imagen de arriba, los tres qubits superiores forman el registro de entrada y el qubit inferior es el registro de salida. Podemos ver qué estados de entrada dan qué salida en la siguiente tabla:\n",
+        "\n",
+        "Estados de entrada que devuelven 0 | Estados de entrada que devuelven 1\n",
+        ":-: | :-:\n",
+        "000 | 001\n",
+        "011 | 100\n",
+        "101 | 010\n",
+        "110 | 111\n",
+        "\n",
+        "Podemos cambiar los resultados mientras los mantenemos balanceados envolviendo los controles seleccionados en compuertas X. Por ejemplo, ve el circuito y su tabla de resultados a continuación:\n",
+        "\n",
+        "![otro_circuito_equilibrado](images/deutsch_balanced2.svg)\n",
+        "\n",
+        "Estados de entrada que devuelven 0 | Estados de entrada que devuelven 1\n",
+        ":-: | :-:\n",
+        "001 | 000\n",
+        "010 | 011\n",
+        "100 | 101\n",
+        "111 | 110"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 4. Qiskit Implementation <a id=\"implementation\"></a>\n",
+        "\n",
+        "Ahora implementamos el algoritmo de Deutsch-Jozsa para el ejemplo de una función de tres bits, con oráculos constantes y balanceados. Primero hagamos nuestras importaciones:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 2,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ],
+        "id": "gl_rX6gqlmTrE"
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "# initialization\n",
+        "import numpy as np\n",
+        "\n",
+        "# importing Qiskit\n",
+        "from qiskit import IBMQ, Aer\n",
+        "from qiskit.providers.ibmq import least_busy\n",
+        "from qiskit import QuantumCircuit, transpile\n",
+        "\n",
+        "# import basic plot tools\n",
+        "from qiskit.visualization import plot_histogram"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "A continuación, establecemos el tamaño del registro de entrada para nuestro oráculo:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 3,
+      "metadata": {
+        "id": "gl_JYIuGX7k8X"
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "# set the length of the n-bit input string. \n",
+        "n = 3"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 4.1 Constant Oracle <a id=\"const_oracle\"></a>\n",
+        "\n",
+        "Comencemos creando un oráculo constante, en este caso la entrada no tiene efecto en la salida, por lo que simplemente establecemos aleatoriamente el qubit de salida en 0 o 1:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 4,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ],
+        "id": "gl_QFqzAYV0bx"
+      },
+      "outputs": [
+        {
+          "data": {
+            "image/svg+xml": [
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+            ],
+            "text/plain": [
+              "<Figure size 116.697x264.88 with 1 Axes>"
+            ]
+          },
+          "execution_count": 4,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# set the length of the n-bit input string. \n",
+        "n = 3\n",
+        "\n",
+        "const_oracle = QuantumCircuit(n+1)\n",
+        "\n",
+        "output = np.random.randint(2)\n",
+        "if output == 1:\n",
+        "    const_oracle.x(n)\n",
+        "\n",
+        "const_oracle.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_Nxhnpw1RLq"
+      },
+      "source": [
+        "### 4.2 Balanced Oracle <a id='balanced_oracle'></a>"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 5,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "balanced_oracle = QuantumCircuit(n+1)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "A continuación, creamos un oráculo balanceado. Como vimos en la sección 1b, podemos generar un oráculo balanceado realizando CNOT con cada qubit de entrada como control y el bit de salida como objetivo. Podemos variar los estados de entrada que dan 0 o 1 envolviendo algunos de los controles en compuertas X. Primero elijamos una cadena binaria de longitud `n` que dicte qué controles ajustar:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 6,
+      "metadata": {
+        "scrolled": true
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "b_str = \"101\""
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Ahora que tenemos esta cadena, podemos usarla como clave para colocar nuestras compuertas X. Para cada qubit en nuestro circuito, colocamos una compuerta X si el dígito correspondiente en `b_str` es `1` , o no hacemos nada si el dígito es `0` ."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 7,
+      "metadata": {
+        "id": "gl_PXIMFKghkl"
+      },
+      "outputs": [
+        {
+          "data": {
+            "image/svg+xml": [
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+            ],
+            "text/plain": [
+              "<Figure size 146.797x264.88 with 1 Axes>"
+            ]
+          },
+          "execution_count": 7,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "balanced_oracle = QuantumCircuit(n+1)\n",
+        "b_str = \"101\"\n",
+        "\n",
+        "# Place X-gates\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "balanced_oracle.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "A continuación, hacemos nuestras compuertas NOT controladas, usando cada qubit de entrada como control y el qubit de salida como objetivo:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 8,
+      "metadata": {
+        "id": "gl_av8QoWOFUL"
+      },
+      "outputs": [
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+            ],
+            "text/plain": [
+              "<Figure size 447.797x264.88 with 1 Axes>"
+            ]
+          },
+          "execution_count": 8,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "balanced_oracle = QuantumCircuit(n+1)\n",
+        "b_str = \"101\"\n",
+        "\n",
+        "# Place X-gates\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "\n",
+        "# Use barrier as divider\n",
+        "balanced_oracle.barrier()\n",
+        "\n",
+        "# Controlled-NOT gates\n",
+        "for qubit in range(n):\n",
+        "    balanced_oracle.cx(qubit, n)\n",
+        "\n",
+        "balanced_oracle.barrier()\n",
+        "balanced_oracle.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Finalmente, repetimos el código de dos celdas en adelante para terminar de envolver los controles en compuertas X:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 9,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ],
+        "id": "gl_9FdkrUrWQK"
+      },
+      "outputs": [
+        {
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+            ],
+            "text/plain": [
+              "<Figure size 507.997x264.88 with 1 Axes>"
+            ]
+          },
+          "execution_count": 9,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "balanced_oracle = QuantumCircuit(n+1)\n",
+        "b_str = \"101\"\n",
+        "\n",
+        "# Place X-gates\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "\n",
+        "# Use barrier as divider\n",
+        "balanced_oracle.barrier()\n",
+        "\n",
+        "# Controlled-NOT gates\n",
+        "for qubit in range(n):\n",
+        "    balanced_oracle.cx(qubit, n)\n",
+        "\n",
+        "balanced_oracle.barrier()\n",
+        "\n",
+        "# Place X-gates\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "\n",
+        "# Show oracle\n",
+        "balanced_oracle.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "We have just created a balanced oracle! All that's left to do is see if the Deutsch-Jozsa algorithm can solve it.\n",
+        "\n",
+        "### 4.3 The Full Algorithm <a id=\"full_alg\"></a>\n",
+        "\n",
+        "Ahora vamos a poner todo junto. Este primer paso en el algoritmo es inicializar los qubits de entrada en el estado $|{+}\\rangle$ y el qubit de salida en el estado $|{-}\\rangle$:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 10,
+      "metadata": {
+        "id": "gl_a2WivaXh1e"
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 206.997x325.08 with 1 Axes>"
+            ]
+          },
+          "execution_count": 10,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "dj_circuit = QuantumCircuit(n+1, n)\n",
+        "\n",
+        "# Apply H-gates\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "\n",
+        "# Put qubit in state |->\n",
+        "dj_circuit.x(n)\n",
+        "dj_circuit.h(n)\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "A continuación, apliquemos el oráculo. Aquí aplicamos el `balanced_oracle` que creamos arriba:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 13,
+      "metadata": {
+        "scrolled": true,
+        "id": "gl_qMpiqjfJFE"
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 568.197x325.08 with 1 Axes>"
+            ]
+          },
+          "execution_count": 13,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "dj_circuit = QuantumCircuit(n+1, n)\n",
+        "\n",
+        "# Apply H-gates\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "\n",
+        "# Put qubit in state |->\n",
+        "dj_circuit.x(n)\n",
+        "dj_circuit.h(n)\n",
+        "\n",
+        "# Add oracle\n",
+        "dj_circuit = dj_circuit.compose(balanced_oracle)\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_SqGzjcPuPf"
+      },
+      "source": [
+        "Finally, we perform H-gates on the $n$-input qubits, and measure our input register:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 14,
+      "metadata": {
+        "scrolled": true,
+        "id": "gl_xF64CoBohj"
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 869.197x325.08 with 1 Axes>"
+            ]
+          },
+          "execution_count": 14,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "dj_circuit = QuantumCircuit(n+1, n)\n",
+        "\n",
+        "# Apply H-gates\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "\n",
+        "# Put qubit in state |->\n",
+        "dj_circuit.x(n)\n",
+        "dj_circuit.h(n)\n",
+        "\n",
+        "# Add oracle\n",
+        "dj_circuit = dj_circuit.compose(balanced_oracle)\n",
+        "\n",
+        "# Repeat H-gates\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "dj_circuit.barrier()\n",
+        "\n",
+        "# Measure\n",
+        "for i in range(n):\n",
+        "    dj_circuit.measure(i, i)\n",
+        "\n",
+        "# Display circuit\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Veamos la salida:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 15,
+      "metadata": {
+        "id": "gl_hHRbe2mfeB"
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 15,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# use local simulator\n",
+        "aer_sim = Aer.get_backend('aer_simulator')\n",
+        "results = aer_sim.run(dj_circuit).result()\n",
+        "answer = results.get_counts()\n",
+        "\n",
+        "plot_histogram(answer)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Podemos ver a partir de los resultados anteriores que tenemos un 0 % de probabilidad de medir `000` . Esto predice correctamente que la función está balanceada.\n",
+        "\n",
+        "### 4.4 Generalised Circuits <a id=\"general_circs\"></a>\n",
+        "\n",
+        "Below, we provide a generalised function that creates Deutsch-Jozsa oracles and turns them into quantum gates. It takes the `case`, (either `'balanced'` or '`constant`', and `n`, the size of the input register:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 16,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ],
+        "id": "gl_TcWIz08MQs"
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "def dj_oracle(case, n):\n",
+        "    # We need to make a QuantumCircuit object to return\n",
+        "    # This circuit has n+1 qubits: the size of the input,\n",
+        "    # plus one output qubit\n",
+        "    oracle_qc = QuantumCircuit(n+1)\n",
+        "    \n",
+        "    # First, let's deal with the case in which oracle is balanced\n",
+        "    if case == \"balanced\":\n",
+        "        # First generate a random number that tells us which CNOTs to\n",
+        "        # wrap in X-gates:\n",
+        "        b = np.random.randint(1,2**n)\n",
+        "        # Next, format 'b' as a binary string of length 'n', padded with zeros:\n",
+        "        b_str = format(b, '0'+str(n)+'b')\n",
+        "        # Next, we place the first X-gates. Each digit in our binary string \n",
+        "        # corresponds to a qubit, if the digit is 0, we do nothing, if it's 1\n",
+        "        # we apply an X-gate to that qubit:\n",
+        "        for qubit in range(len(b_str)):\n",
+        "            if b_str[qubit] == '1':\n",
+        "                oracle_qc.x(qubit)\n",
+        "        # Do the controlled-NOT gates for each qubit, using the output qubit \n",
+        "        # as the target:\n",
+        "        for qubit in range(n):\n",
+        "            oracle_qc.cx(qubit, n)\n",
+        "        # Next, place the final X-gates\n",
+        "        for qubit in range(len(b_str)):\n",
+        "            if b_str[qubit] == '1':\n",
+        "                oracle_qc.x(qubit)\n",
+        "\n",
+        "    # Case in which oracle is constant\n",
+        "    if case == \"constant\":\n",
+        "        # First decide what the fixed output of the oracle will be\n",
+        "        # (either always 0 or always 1)\n",
+        "        output = np.random.randint(2)\n",
+        "        if output == 1:\n",
+        "            oracle_qc.x(n)\n",
+        "    \n",
+        "    oracle_gate = oracle_qc.to_gate()\n",
+        "    oracle_gate.name = \"Oracle\" # To show when we display the circuit\n",
+        "    return oracle_gate"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "También vamos a crear una función que tome esta compuerta del oráculo y realice el algoritmo Deutsch-Jozsa en ella:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 17,
+      "metadata": {
+        "scrolled": true,
+        "tags": [
+          "thebelab-init"
+        ],
+        "id": "gl_lBwrELwLiH"
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "def dj_algorithm(oracle, n):\n",
+        "    dj_circuit = QuantumCircuit(n+1, n)\n",
+        "    # Set up the output qubit:\n",
+        "    dj_circuit.x(n)\n",
+        "    dj_circuit.h(n)\n",
+        "    # And set up the input register:\n",
+        "    for qubit in range(n):\n",
+        "        dj_circuit.h(qubit)\n",
+        "    # Let's append the oracle gate to our circuit:\n",
+        "    dj_circuit.append(oracle, range(n+1))\n",
+        "    # Finally, perform the H-gates again and measure:\n",
+        "    for qubit in range(n):\n",
+        "        dj_circuit.h(qubit)\n",
+        "    \n",
+        "    for i in range(n):\n",
+        "        dj_circuit.measure(i, i)\n",
+        "    \n",
+        "    return dj_circuit"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Finalmente, usemos estas funciones para jugar con el algoritmo:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 18,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 628.397x385.28 with 1 Axes>"
+            ]
+          },
+          "execution_count": 18,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "n = 4\n",
+        "oracle_gate = dj_oracle('balanced', n)\n",
+        "dj_circuit = dj_algorithm(oracle_gate, n)\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_v0mVqiKigu"
+      },
+      "source": [
+        "And see the results of running this circuit:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 19,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 19,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "transpiled_dj_circuit = transpile(dj_circuit, aer_sim)\n",
+        "results = aer_sim.run(transpiled_dj_circuit).result()\n",
+        "answer = results.get_counts()\n",
+        "plot_histogram(answer)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 5. Experiment with Real Devices <a id=\"device\"></a>\n",
+        "\n",
+        "Podemos ejecutar el circuito en el dispositivo real como se muestra a continuación. Primero buscamos el dispositivo menos ocupado que pueda manejar nuestro circuito."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 20,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ],
+        "id": "gl_fDFLPSWsDV"
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "least busy backend:  ibmq_belem\n"
+          ]
+        }
+      ],
+      "source": [
+        "# Load our saved IBMQ accounts and get the least busy backend device with greater than or equal to (n+1) qubits\n",
+        "IBMQ.load_account()\n",
+        "provider = IBMQ.get_provider(hub='ibm-q')\n",
+        "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= (n+1) and\n",
+        "                                   not x.configuration().simulator and x.status().operational==True))\n",
+        "print(\"least busy backend: \", backend)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 21,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ]
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Job Status: job has successfully run\n"
+          ]
+        }
+      ],
+      "source": [
+
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 22,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ],
+        "id": "gl_RyV9hD60vD"
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 22,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# Get the results of the computation\n",
+        "results = job.result()\n",
+        "answer = results.get_counts()\n",
+        "\n",
+        "plot_histogram(answer)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Como podemos ver, el resultado más probable es `1111` . Los otros resultados se deben a errores en el cálculo cuántico. "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_w9ipMJQDPZ"
+      },
+      "source": [
+        "## 6. Problems <a id='problems'></a>\n",
+        "\n",
+        "1. Are you able to create a balanced or constant oracle of a different form?\n",
+        "\n",
+        "2. The function `dj_problem_oracle` (below) returns a Deutsch-Jozsa oracle for `n = 4` in the form of a gate. The gate takes 5 qubits as input where the final qubit (`q_4`) is the output qubit (as with the example oracles above). You can get different oracles by giving `dj_problem_oracle` different integers between 1 and 5. Use the Deutsch-Jozsa algorithm to decide whether each oracle is balanced or constant (**Note:** It is highly recommended you try this example using the `aer_simulator` instead of a real device)."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "from qiskit_textbook.problems import dj_problem_oracle\n",
+        "oracle = dj_problem_oracle(1)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 7. References <a id=\"references\"></a>\n",
+        "\n",
+        "1. David Deutsch and Richard Jozsa (1992). \"Rapid solutions of problems by quantum computation\". Proceedings of the Royal Society of London A. 439: 553–558.  [doi:10.1098/rspa.1992.0167](https://doi.org/10.1098%2Frspa.1992.0167).\n",
+        "2. R. Cleve; A. Ekert; C. Macchiavello; M. Mosca (1998). \"Quantum algorithms revisited\". Proceedings of the Royal Society of London A. 454: 339–354. [doi:10.1098/rspa.1998.0164](https://doi.org/10.1098%2Frspa.1998.0164)."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 23,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "name": "stderr",
+          "output_type": "stream",
+          "text": [
+            "/usr/local/anaconda3/envs/terra-unstable/lib/python3.9/site-packages/qiskit/aqua/__init__.py:86: DeprecationWarning: The package qiskit.aqua is deprecated. It was moved/refactored to qiskit-terra For more information see <https://github.com/Qiskit/qiskit-aqua/blob/main/README.md#migration-guide>\n",
+            "  warn_package('aqua', 'qiskit-terra')\n"
+          ]
+        },
+        {
+          "data": {
+            "text/html": [
+              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.19.0</td></tr><tr><td><code>qiskit-aer</code></td><td>0.9.1</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.6.0</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.17.0</td></tr><tr><td><code>qiskit-aqua</code></td><td>0.9.5</td></tr><tr><td><code>qiskit</code></td><td>0.31.0</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.9.7</td></tr><tr><td>Python compiler</td><td>Clang 10.0.0 </td></tr><tr><td>Python build</td><td>default, Sep 16 2021 08:50:36</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>32.0</td></tr><tr><td colspan='2'>Fri Nov 05 14:18:55 2021 GMT</td></tr></table>"
+            ],
+            "text/plain": [
+              "<IPython.core.display.HTML object>"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "import qiskit.tools.jupyter\n",
+        "%qiskit_version_table"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 2
+}

From 229ac73dfbddabb62aee36af8d0c2b816a17f6dc Mon Sep 17 00:00:00 2001
From: Claudia Zendejas-Morales <clausia@ciencias.unam.mx>
Date: Tue, 14 Jun 2022 05:05:04 +0000
Subject: [PATCH 54/62] Translate deutsch-jozsa.ipynb via GitLocalize

---
 .../es/ch-algorithms/deutsch-jozsa.ipynb      | 213 ++++++++----------
 1 file changed, 99 insertions(+), 114 deletions(-)

diff --git a/translations/es/ch-algorithms/deutsch-jozsa.ipynb b/translations/es/ch-algorithms/deutsch-jozsa.ipynb
index e61f80feb..8cd553e42 100644
--- a/translations/es/ch-algorithms/deutsch-jozsa.ipynb
+++ b/translations/es/ch-algorithms/deutsch-jozsa.ipynb
@@ -22,10 +22,9 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_uAozTzR78t"
       },
       "source": [
-        "## 1. Introduction <a id='introduction'></a>"
+        "## 1. Introducción <a id=\"introduction\"></a>"
       ]
     },
     {
@@ -41,7 +40,7 @@
       "metadata": {
       },
       "source": [
-        "### 1.1 Deutsch-Jozsa Problem <a id=\"djproblem\"> </a>\n",
+        "### 1.1 Problema de Deutsch-Jozsa <a id=\"djproblem\"> </a>\n",
         "\n",
         "Tenemos una función booleana oculta $f$, que toma como entrada una cadena de bits y devuelve $0$ o $1$, es decir:\n",
         "\n",
@@ -51,7 +50,7 @@
         "\n",
         "Ten en cuenta que el problema de Deutsch-Jozsa es una extensión de $n$ bits del problema de Deutsch de un solo bit.\n",
         "\n",
-        "### 1.2 The Classical Solution <a id=\"classical-solution\"> </a>\n",
+        "### 1.2 La Solución Clásica <a id=\"classical-solution\"> </a>\n",
         "\n",
         "Clásicamente, en el mejor de los casos, dos consultas al oráculo pueden determinar si la función booleana oculta, $f(x)$, es balanceada: por ejemplo, si obtenemos ambas $f(0,0,0,...)\\rightarrow 0$ y $f(1,0,0,...) \\rightarrow 1$, entonces sabemos que la función está balanceada, ya que hemos obtenido las dos salidas diferentes.\n",
         "\n",
@@ -59,7 +58,7 @@
         "\n",
         "$$ P_\\textrm{constant}(k) = 1 - \\frac{1}{2^{k-1}} \\qquad \\textrm{para } 1 &lt; k \\leq 2^{n-1}$$\n",
         "\n",
-        "Realistically, we could opt to truncate our classical algorithm early, say if we were over x% confident. But if we want to be 100% confident, we would need to check $2^{n-1}+1$ inputs."
+        "Siendo realistas, podríamos optar por truncar de manera temprana nuestro algoritmo clásico, digamos si tuviéramos más de un x% de confianza. Pero si queremos estar 100% seguros, tendríamos que verificar las entradas de $2^{n-1}+1$."
       ]
     },
     {
@@ -67,9 +66,9 @@
       "metadata": {
       },
       "source": [
-        "### 1.3 Quantum Solution <a id=\"quantum-solution\"> </a>\n",
+        "### 1.3 Solución Cuántica <a id=\"quantum-solution\"> </a>\n",
         "\n",
-        "Using a quantum computer, we can solve this problem with 100% confidence after only one call to the function $f(x)$, provided we have the function $f$ implemented as a quantum oracle, which maps the state $\\vert x\\rangle \\vert y\\rangle $ to $ \\vert x\\rangle \\vert y \\oplus f(x)\\rangle$, where $\\oplus$ is addition modulo $2$. Below is the generic circuit for the Deutsch-Jozsa algorithm.\n",
+        "Usando una computadora cuántica, podemos resolver este problema con un 100% de confianza después de una sola llamada a la función $f(x)$, siempre que tengamos la función $f$ implementada como un oráculo cuántico, que mapea el estado $\\vert x \\rangle \\vert y\\rangle $ a $ \\vert x\\rangle \\vert y \\oplus f(x)\\rangle$, donde $\\oplus$ es la adición de módulo $2$. A continuación se muestra el circuito genérico para el algoritmo Deutsch-Jozsa.\n",
         "\n",
         "![imagen1](images/deutsch_steps.png)\n",
         "\n",
@@ -84,7 +83,7 @@
         "   \n",
         "\n",
         "\n",
-        "   <li>         Apply a Hadamard gate to each qubit: </li>\n",
+        "   <li>Aplica una compuerta Hadamard a cada qubit:</li>\n",
         "\n",
         "\n",
         "$$\\vert \\psi_1 \\rangle = \\frac{1}{\\sqrt{2^{n+1}}}\\sum_{x=0}^{2^n-1} \\vert x\\rangle \\left(|0\\rangle - |1 \\rangle \\right)$$\n",
@@ -100,7 +99,7 @@
         "   \n",
         "\n",
         "\n",
-        "   <li>        At this point the second single qubit register may be ignored. Apply a Hadamard gate to each qubit in the first register:         $$         \\begin{aligned}             \\lvert \\psi_3 \\rangle                  &amp; = \\frac{1}{2^n}\\sum_{x=0}^{2^n-1}(-1)^{f(x)}                     \\left[ \\sum_{y=0}^{2^n-1}(-1)^{x \\cdot y}                      \\vert y \\rangle \\right] \\\\                 &amp; = \\frac{1}{2^n}\\sum_{y=0}^{2^n-1}                     \\left[ \\sum_{x=0}^{2^n-1}(-1)^{f(x)}(-1)^{x \\cdot y} \\right]                     \\vert y \\rangle         \\end{aligned}         $$ </li>\n",
+        "   <li>En este punto, se puede ignorar el segundo registro de un solo qubit. Aplica una compuerta Hadamard a cada qubit en el primer registro: $$ \\begin{aligned} \\lvert \\psi_3 \\rangle &amp; = \\frac{1}{2^n}\\sum_{x=0}^{2^n-1}(-1)^{f(x)} \\left[ \\sum_{y=0}^{2^n-1}(-1)^{x \\cdot y} \\vert y \\rangle \\right] \\\\ &amp; = \\frac{1}{2^n}\\sum_{y=0}^{2^n-1} \\left[ \\sum_{x=0}^{2^n-1}(-1)^{f(x)}(-1)^{x \\cdot y} \\right] \\vert y \\rangle \\end{aligned} $$</li>\n",
         "\n",
         "\n",
         "donde $x \\cdot y = x_0y_0 \\oplus x_1y_1 \\oplus \\ldots \\oplus x_{n-1}y_{n-1}$ es la suma del producto bit a bit.\n",
@@ -114,11 +113,11 @@
         "\n",
         "\n",
         "\n",
-        "### 1.4 Why Does This Work? <a id=\"why-does-this-work\"> </a>\n",
+        "### 1.4 ¿Por qué funciona esto? <a id=\"why-does-this-work\"> </a>\n",
         "\n",
         "- **    Oráculo Constante**\n",
         "\n",
-        "When the oracle is *constant*, it has no effect (up to a global phase) on the input qubits, and the quantum states before and after querying the oracle are the same. Since the H-gate is its own inverse, in Step 4 we reverse Step 2 to obtain the initial quantum state of $|00\\dots 0\\rangle$ in the first register.\n",
+        "Cuando el oráculo es *constante*, no tiene efecto (hasta una fase global) en los qubits de entrada, y los estados cuánticos antes y después de consultar el oráculo son los mismos. Dado que la compuerta H es su propio inverso, en el Paso 4 invertimos el Paso 2 para obtener el estado cuántico inicial de $|00\\dots 0\\rangle$ en el primer registro.\n",
         "\n",
         "# $$ H^{\\otimes n}\\begin{bmatrix} 1 \\ 0 \\ 0 \\ \\vdots \\ 0 \\end{bmatrix}\n",
         "\n",
@@ -126,9 +125,9 @@
         "\n",
         "\\begin{bmatrix} 1 \\ 0 \\ 0 \\ \\vdots \\ 0 \\end{bmatrix} $$\n",
         "\n",
-        "- **Balanced Oracle**\n",
+        "- **Oráculo Balanceado**\n",
         "\n",
-        "After step 2, our input register is an equal superposition of all the states in the computational basis. When the oracle is *balanced*, phase kickback adds a negative phase to exactly half these states:\n",
+        "Después del paso 2, nuestro registro de entrada es una superposición igual de todos los estados en la base computacional. Cuando el oráculo está *balanceado*, el retroceso de fase añade una fase negativa a exactamente la mitad de estos estados:\n",
         "\n",
         "# $$ U_f \\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix}\n",
         "\n",
@@ -142,11 +141,11 @@
       "metadata": {
       },
       "source": [
-        "## 2. Worked Example  <a id=\"example\"></a>\n",
+        "## 2. Ejemplo Resuelto <a id=\"example\"></a>\n",
         "\n",
         "Veamos un ejemplo específico para una función balanceada de dos bits:\n",
         "\n",
-        "Consider a two-bit function $f(x_0,x_1)=x_0 \\oplus x_1$ such that\n",
+        "Considera una función de dos bits $f(x_0,x_1)=x_0 \\oplus x_1$ tal que:\n",
         "\n",
         "$f(0,0)=0$\n",
         "\n",
@@ -174,15 +173,15 @@
         "   <li>Aplicar Hadamard en todos los qubits</li>\n",
         "\n",
         "\n",
-        "$$\\lvert \\psi_1 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle + \\lvert 0 1 \\rangle + \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)*{01} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)*{2}  $$\n",
+        "$$\\lvert \\psi_1 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle + \\lvert 0 1 \\rangle + \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)*{01} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)*{2} $$\n",
         "\n",
         "   \n",
         "\n",
         "\n",
-        "   <li> The oracle function can be implemented as $\\text{Q}_f = CX_{02}CX_{12}$,            $$        \\begin{aligned}             \\lvert \\psi_2 \\rangle =  \\frac{1}{2\\sqrt{2}} \\left[ \\lvert 0 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 0 \\oplus 0 \\rangle - \\lvert 1 \\oplus 0 \\oplus 0 \\rangle \\right)_{2} \\\\                   + \\lvert 0 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 0 \\oplus 1 \\rangle - \\lvert 1 \\oplus 0 \\oplus 1 \\rangle \\right)_{2} \\\\                   + \\lvert 1 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 1 \\oplus 0 \\rangle - \\lvert 1 \\oplus 1 \\oplus 0 \\rangle \\right)_{2} \\\\                   + \\lvert 1 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 1 \\oplus 1 \\rangle - \\lvert 1 \\oplus 1 \\oplus 1 \\rangle \\right)_{2} \\right]         \\end{aligned}          $$    </li>\n",
+        "   <li>La función del oráculo puede ser implementada como $\\text{Q}_f = CX_{02}CX_{12}$, $$ \\begin{aligned} \\lvert \\psi_2 \\rangle = \\frac{1}{2\\sqrt{2}} \\left[ \\lvert 0 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 0 \\oplus 0 \\rangle - \\lvert 1 \\oplus 0 \\oplus 0 \\rangle \\right)_{2} \\\\ + \\lvert 0 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 0 \\oplus 1 \\rangle - \\lvert 1 \\oplus 0 \\oplus 1 \\rangle \\right)_{2} \\\\ + \\lvert 1 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 1 \\oplus 0 \\rangle - \\lvert 1 \\oplus 1 \\oplus 0 \\rangle \\right)_{2} \\\\ + \\lvert 1 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 1 \\oplus 1 \\rangle - \\lvert 1 \\oplus 1 \\oplus 1 \\rangle \\right)_{2} \\right] \\end{aligned} $$</li>\n",
         "\n",
         "\n",
-        "   <li>Simplifying this, we get the following:         $$        \\begin{aligned}         \\lvert \\psi_2 \\rangle &amp; = \\frac{1}{2\\sqrt{2}} \\left[ \\lvert 0 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} - \\lvert 0 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert  1 \\rangle \\right)_{2} - \\lvert 1 0 \\rangle_{01} \\otimes \\left( \\lvert 0  \\rangle - \\lvert 1 \\rangle \\right)_{2} + \\lvert 1 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2}  \\right] \\\\         &amp; = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle - \\lvert 0 1 \\rangle - \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)_{01} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} \\\\         &amp; = \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{0} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{1} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2}         \\end{aligned}         $$    </li>\n",
+        "   <li>Simplificando esto, obtenemos lo siguiente: $$ \\begin{aligned} \\lvert \\psi_2 \\rangle &amp; = \\frac{1}{2\\sqrt{2}} \\left[ \\lvert 0 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} - \\lvert 0 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} - \\lvert 1 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} + \\lvert 1 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} \\right] \\\\ &amp; = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle - \\lvert 0 1 \\rangle - \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)_{01} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} \\\\ &amp; = \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{0} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{1} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} \\end{aligned} $$</li>\n",
         "\n",
         "\n",
         "   <li>Aplicar Hadamard en el primer registro</li>\n",
@@ -219,14 +218,13 @@
       "metadata": {
       },
       "source": [
-        "## 3. Creating Quantum Oracles <a id=\"creating-quantum-oracles\"> </a>\n",
+        "## 3. Creando Oráculos Cuánticos <a id=\"creating-quantum-oracles\"> </a>\n",
         "\n",
         "Veamos algunas formas diferentes en que podemos crear un oráculo cuántico.\n",
         "\n",
         "Para una función constante, es simple:\n",
         "\n",
-        "$\\qquad$ 1. if f(x) = 0, then apply the $I$ gate to the qubit in register 2.\n",
-        " $\\qquad$ 2. if f(x) = 1, then apply the $X$ gate to the qubit in register 2.\n",
+        "$\\qquad$ 1. Si f(x) = 0, entonces aplica la compuerta $I$ al qubit en el registro 2.<br> $\\qquad$ 2. Si f(x) = 1, entonces aplica la compuerta $X$ al qubit en el registro 2.\n",
         "\n",
         "Para una función balanceada, hay muchos circuitos diferentes que podemos crear. Una de las formas en que podemos garantizar que nuestro circuito esté balanceado es realizando un CNOT para cada qubit en el registro 1, con el qubit en el registro 2 como objetivo. Por ejemplo:\n",
         "\n",
@@ -258,7 +256,7 @@
       "metadata": {
       },
       "source": [
-        "## 4. Qiskit Implementation <a id=\"implementation\"></a>\n",
+        "## 4. Implementación en Qiskit <a id=\"implementation\"></a>\n",
         "\n",
         "Ahora implementamos el algoritmo de Deutsch-Jozsa para el ejemplo de una función de tres bits, con oráculos constantes y balanceados. Primero hagamos nuestras importaciones:"
       ]
@@ -269,22 +267,21 @@
       "metadata": {
         "tags": [
           "thebelab-init"
-        ],
-        "id": "gl_rX6gqlmTrE"
+        ]
       },
       "outputs": [
 
       ],
       "source": [
-        "# initialization\n",
+        "# inicialización\n",
         "import numpy as np\n",
         "\n",
-        "# importing Qiskit\n",
+        "# importando Qiskit\n",
         "from qiskit import IBMQ, Aer\n",
         "from qiskit.providers.ibmq import least_busy\n",
         "from qiskit import QuantumCircuit, transpile\n",
         "\n",
-        "# import basic plot tools\n",
+        "# importar herramientas básicas de graficación\n",
         "from qiskit.visualization import plot_histogram"
       ]
     },
@@ -300,13 +297,12 @@
       "cell_type": "code",
       "execution_count": 3,
       "metadata": {
-        "id": "gl_JYIuGX7k8X"
       },
       "outputs": [
 
       ],
       "source": [
-        "# set the length of the n-bit input string. \n",
+        "# establece la longitud de la cadena de entrada de n bits.\n",
         "n = 3"
       ]
     },
@@ -315,7 +311,7 @@
       "metadata": {
       },
       "source": [
-        "### 4.1 Constant Oracle <a id=\"const_oracle\"></a>\n",
+        "### 4.1 Oráculo Constante <a id=\"const_oracle\"></a>\n",
         "\n",
         "Comencemos creando un oráculo constante, en este caso la entrada no tiene efecto en la salida, por lo que simplemente establecemos aleatoriamente el qubit de salida en 0 o 1:"
       ]
@@ -326,8 +322,7 @@
       "metadata": {
         "tags": [
           "thebelab-init"
-        ],
-        "id": "gl_QFqzAYV0bx"
+        ]
       },
       "outputs": [
         {
@@ -346,7 +341,7 @@
         }
       ],
       "source": [
-        "# set the length of the n-bit input string. \n",
+        "# establece la longitud de la cadena de entrada de n bits.\n",
         "n = 3\n",
         "\n",
         "const_oracle = QuantumCircuit(n+1)\n",
@@ -361,10 +356,9 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_Nxhnpw1RLq"
       },
       "source": [
-        "### 4.2 Balanced Oracle <a id='balanced_oracle'></a>"
+        "### 4.2 Oráculo Balanceado <a id=\"balanced_oracle\"></a>"
       ]
     },
     {
@@ -412,7 +406,6 @@
       "cell_type": "code",
       "execution_count": 7,
       "metadata": {
-        "id": "gl_PXIMFKghkl"
       },
       "outputs": [
         {
@@ -434,7 +427,7 @@
         "balanced_oracle = QuantumCircuit(n+1)\n",
         "b_str = \"101\"\n",
         "\n",
-        "# Place X-gates\n",
+        "# Colocar compuertas X\n",
         "for qubit in range(len(b_str)):\n",
         "    if b_str[qubit] == '1':\n",
         "        balanced_oracle.x(qubit)\n",
@@ -453,7 +446,6 @@
       "cell_type": "code",
       "execution_count": 8,
       "metadata": {
-        "id": "gl_av8QoWOFUL"
       },
       "outputs": [
         {
@@ -475,15 +467,15 @@
         "balanced_oracle = QuantumCircuit(n+1)\n",
         "b_str = \"101\"\n",
         "\n",
-        "# Place X-gates\n",
+        "# Colocar compuertas X\n",
         "for qubit in range(len(b_str)):\n",
         "    if b_str[qubit] == '1':\n",
         "        balanced_oracle.x(qubit)\n",
         "\n",
-        "# Use barrier as divider\n",
+        "# Usar una barrera como divisor\n",
         "balanced_oracle.barrier()\n",
         "\n",
-        "# Controlled-NOT gates\n",
+        "# Compuertas NOT controladas\n",
         "for qubit in range(n):\n",
         "    balanced_oracle.cx(qubit, n)\n",
         "\n",
@@ -505,8 +497,7 @@
       "metadata": {
         "tags": [
           "thebelab-init"
-        ],
-        "id": "gl_9FdkrUrWQK"
+        ]
       },
       "outputs": [
         {
@@ -528,26 +519,26 @@
         "balanced_oracle = QuantumCircuit(n+1)\n",
         "b_str = \"101\"\n",
         "\n",
-        "# Place X-gates\n",
+        "# Colocar compuertas X\n",
         "for qubit in range(len(b_str)):\n",
         "    if b_str[qubit] == '1':\n",
         "        balanced_oracle.x(qubit)\n",
         "\n",
-        "# Use barrier as divider\n",
+        "# Usar una barrera como divisor\n",
         "balanced_oracle.barrier()\n",
         "\n",
-        "# Controlled-NOT gates\n",
+        "# Compuertas NOT controladas\n",
         "for qubit in range(n):\n",
         "    balanced_oracle.cx(qubit, n)\n",
         "\n",
         "balanced_oracle.barrier()\n",
         "\n",
-        "# Place X-gates\n",
+        "# Colocar compuertas X\n",
         "for qubit in range(len(b_str)):\n",
         "    if b_str[qubit] == '1':\n",
         "        balanced_oracle.x(qubit)\n",
         "\n",
-        "# Show oracle\n",
+        "# Mostrar el oráculo\n",
         "balanced_oracle.draw()"
       ]
     },
@@ -556,9 +547,9 @@
       "metadata": {
       },
       "source": [
-        "We have just created a balanced oracle! All that's left to do is see if the Deutsch-Jozsa algorithm can solve it.\n",
+        "¡Acabamos de crear un oráculo balanceado! Todo lo que queda por hacer es ver si el algoritmo Deutsch-Jozsa puede resolverlo.\n",
         "\n",
-        "### 4.3 The Full Algorithm <a id=\"full_alg\"></a>\n",
+        "### 4.3 El Algoritmo Completo <a id=\"full_alg\"></a>\n",
         "\n",
         "Ahora vamos a poner todo junto. Este primer paso en el algoritmo es inicializar los qubits de entrada en el estado $|{+}\\rangle$ y el qubit de salida en el estado $|{-}\\rangle$:"
       ]
@@ -567,7 +558,6 @@
       "cell_type": "code",
       "execution_count": 10,
       "metadata": {
-        "id": "gl_a2WivaXh1e"
       },
       "outputs": [
         {
@@ -588,11 +578,11 @@
       "source": [
         "dj_circuit = QuantumCircuit(n+1, n)\n",
         "\n",
-        "# Apply H-gates\n",
+        "# Aplicar compuertas H\n",
         "for qubit in range(n):\n",
         "    dj_circuit.h(qubit)\n",
         "\n",
-        "# Put qubit in state |->\n",
+        "# Poner el qubit en el estado |->\n",
         "dj_circuit.x(n)\n",
         "dj_circuit.h(n)\n",
         "dj_circuit.draw()"
@@ -610,8 +600,7 @@
       "cell_type": "code",
       "execution_count": 13,
       "metadata": {
-        "scrolled": true,
-        "id": "gl_qMpiqjfJFE"
+        "scrolled": true
       },
       "outputs": [
         {
@@ -632,15 +621,15 @@
       "source": [
         "dj_circuit = QuantumCircuit(n+1, n)\n",
         "\n",
-        "# Apply H-gates\n",
+        "# Aplicar compuertas H\n",
         "for qubit in range(n):\n",
         "    dj_circuit.h(qubit)\n",
         "\n",
-        "# Put qubit in state |->\n",
+        "# Poner el qubit en el estado |->\n",
         "dj_circuit.x(n)\n",
         "dj_circuit.h(n)\n",
         "\n",
-        "# Add oracle\n",
+        "# Agregar el oráculo\n",
         "dj_circuit = dj_circuit.compose(balanced_oracle)\n",
         "dj_circuit.draw()"
       ]
@@ -648,18 +637,16 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_SqGzjcPuPf"
       },
       "source": [
-        "Finally, we perform H-gates on the $n$-input qubits, and measure our input register:"
+        "Finalmente, aplicamos compuertas H en los qubits de entrada $n$ y medimos nuestro registro de entrada:"
       ]
     },
     {
       "cell_type": "code",
       "execution_count": 14,
       "metadata": {
-        "scrolled": true,
-        "id": "gl_xF64CoBohj"
+        "scrolled": true
       },
       "outputs": [
         {
@@ -680,27 +667,27 @@
       "source": [
         "dj_circuit = QuantumCircuit(n+1, n)\n",
         "\n",
-        "# Apply H-gates\n",
+        "# Aplicar compuertas H\n",
         "for qubit in range(n):\n",
         "    dj_circuit.h(qubit)\n",
         "\n",
-        "# Put qubit in state |->\n",
+        "# Poner el qubit en el estado |->\n",
         "dj_circuit.x(n)\n",
         "dj_circuit.h(n)\n",
         "\n",
-        "# Add oracle\n",
+        "# Agregar el oráculo\n",
         "dj_circuit = dj_circuit.compose(balanced_oracle)\n",
         "\n",
-        "# Repeat H-gates\n",
+        "# Repetir compuertas H\n",
         "for qubit in range(n):\n",
         "    dj_circuit.h(qubit)\n",
         "dj_circuit.barrier()\n",
         "\n",
-        "# Measure\n",
+        "# Medir\n",
         "for i in range(n):\n",
         "    dj_circuit.measure(i, i)\n",
         "\n",
-        "# Display circuit\n",
+        "# Mostrar el circuito\n",
         "dj_circuit.draw()"
       ]
     },
@@ -716,7 +703,6 @@
       "cell_type": "code",
       "execution_count": 15,
       "metadata": {
-        "id": "gl_hHRbe2mfeB"
       },
       "outputs": [
         {
@@ -735,7 +721,7 @@
         }
       ],
       "source": [
-        "# use local simulator\n",
+        "# usar un simulador local\n",
         "aer_sim = Aer.get_backend('aer_simulator')\n",
         "results = aer_sim.run(dj_circuit).result()\n",
         "answer = results.get_counts()\n",
@@ -750,9 +736,9 @@
       "source": [
         "Podemos ver a partir de los resultados anteriores que tenemos un 0 % de probabilidad de medir `000` . Esto predice correctamente que la función está balanceada.\n",
         "\n",
-        "### 4.4 Generalised Circuits <a id=\"general_circs\"></a>\n",
+        "### 4.4 Circuitos Generalizados <a id=\"general_circs\"></a>\n",
         "\n",
-        "Below, we provide a generalised function that creates Deutsch-Jozsa oracles and turns them into quantum gates. It takes the `case`, (either `'balanced'` or '`constant`', and `n`, the size of the input register:"
+        "A continuación, proporcionamos una función generalizada que crea oráculos Deutsch-Jozsa y los convierte en compuertas cuánticas. Toma el `case` , (ya sea `'balanced'` o '`constant`', y `n`, el tamaño del registro de entrada:"
       ]
     },
     {
@@ -761,51 +747,50 @@
       "metadata": {
         "tags": [
           "thebelab-init"
-        ],
-        "id": "gl_TcWIz08MQs"
+        ]
       },
       "outputs": [
 
       ],
       "source": [
         "def dj_oracle(case, n):\n",
-        "    # We need to make a QuantumCircuit object to return\n",
-        "    # This circuit has n+1 qubits: the size of the input,\n",
-        "    # plus one output qubit\n",
+        "    # Necesitamos hacer un objeto QuantumCircuit para devolver\n",
+        "    # Este circuito tiene n+1 qubits: el tamaño de la entrada,\n",
+        "    # más un qubit de salida\n",
         "    oracle_qc = QuantumCircuit(n+1)\n",
         "    \n",
-        "    # First, let's deal with the case in which oracle is balanced\n",
+        "    # Primero, tratemos el caso en el que oráculo está balanceado\n",
         "    if case == \"balanced\":\n",
-        "        # First generate a random number that tells us which CNOTs to\n",
-        "        # wrap in X-gates:\n",
+        "        # Primero genera un número aleatorio que nos diga qué CNOT \n",
+        "        # envolver en compuertas X:\n",
         "        b = np.random.randint(1,2**n)\n",
-        "        # Next, format 'b' as a binary string of length 'n', padded with zeros:\n",
+        "        # A continuación, formatea 'b' como una cadena binaria de longitud 'n', rellenada con ceros:\n",
         "        b_str = format(b, '0'+str(n)+'b')\n",
-        "        # Next, we place the first X-gates. Each digit in our binary string \n",
-        "        # corresponds to a qubit, if the digit is 0, we do nothing, if it's 1\n",
-        "        # we apply an X-gate to that qubit:\n",
+        "        # Después, colocamos las primeras compuertas X. Cada dígito en nuestra cadena binaria\n",
+        "        # corresponde a un qubit, si el dígito es 0, no hacemos nada, si es 1,\n",
+        "        # aplicamos una compuerta X a ese qubit:\n",
         "        for qubit in range(len(b_str)):\n",
         "            if b_str[qubit] == '1':\n",
         "                oracle_qc.x(qubit)\n",
-        "        # Do the controlled-NOT gates for each qubit, using the output qubit \n",
-        "        # as the target:\n",
+        "        # Haz las compuertas NOT controladas para cada qubit, utilizando el qubit de salida\n",
+        "        # como el objetivo:\n",
         "        for qubit in range(n):\n",
         "            oracle_qc.cx(qubit, n)\n",
-        "        # Next, place the final X-gates\n",
+        "        # Luego, coloca las compuertas X finales\n",
         "        for qubit in range(len(b_str)):\n",
         "            if b_str[qubit] == '1':\n",
         "                oracle_qc.x(qubit)\n",
         "\n",
-        "    # Case in which oracle is constant\n",
+        "    # Caso en el que oráculo es constante\n",
         "    if case == \"constant\":\n",
-        "        # First decide what the fixed output of the oracle will be\n",
-        "        # (either always 0 or always 1)\n",
+        "        # Primero decide cuál será la salida fija del oráculo\n",
+        "        # (ya sea siempre 0 o siempre 1)\n",
         "        output = np.random.randint(2)\n",
         "        if output == 1:\n",
         "            oracle_qc.x(n)\n",
         "    \n",
         "    oracle_gate = oracle_qc.to_gate()\n",
-        "    oracle_gate.name = \"Oracle\" # To show when we display the circuit\n",
+        "    oracle_gate.name = \"Oracle\" # Para mostrar cuando presentamos el circuito\n",
         "    return oracle_gate"
       ]
     },
@@ -824,8 +809,7 @@
         "scrolled": true,
         "tags": [
           "thebelab-init"
-        ],
-        "id": "gl_lBwrELwLiH"
+        ]
       },
       "outputs": [
 
@@ -833,15 +817,15 @@
       "source": [
         "def dj_algorithm(oracle, n):\n",
         "    dj_circuit = QuantumCircuit(n+1, n)\n",
-        "    # Set up the output qubit:\n",
+        "    # Configurar el qubit de salida:\n",
         "    dj_circuit.x(n)\n",
         "    dj_circuit.h(n)\n",
-        "    # And set up the input register:\n",
+        "    # Y configurar el registro de entrada:\n",
         "    for qubit in range(n):\n",
         "        dj_circuit.h(qubit)\n",
-        "    # Let's append the oracle gate to our circuit:\n",
+        "    # Agreguemos la compuerta del oráculo a nuestro circuito:\n",
         "    dj_circuit.append(oracle, range(n+1))\n",
-        "    # Finally, perform the H-gates again and measure:\n",
+        "    # Finalmente, ejecutar las compuertas H nuevamente y medir:\n",
         "    for qubit in range(n):\n",
         "        dj_circuit.h(qubit)\n",
         "    \n",
@@ -890,10 +874,9 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_v0mVqiKigu"
       },
       "source": [
-        "And see the results of running this circuit:"
+        "Y observa los resultados de ejecutar este circuito:"
       ]
     },
     {
@@ -929,7 +912,7 @@
       "metadata": {
       },
       "source": [
-        "## 5. Experiment with Real Devices <a id=\"device\"></a>\n",
+        "## 5. Experimenta con Dispositivos Reales <a id=\"device\"></a>\n",
         "\n",
         "Podemos ejecutar el circuito en el dispositivo real como se muestra a continuación. Primero buscamos el dispositivo menos ocupado que pueda manejar nuestro circuito."
       ]
@@ -940,25 +923,24 @@
       "metadata": {
         "tags": [
           "uses-hardware"
-        ],
-        "id": "gl_fDFLPSWsDV"
+        ]
       },
       "outputs": [
         {
           "name": "stdout",
           "output_type": "stream",
           "text": [
-            "least busy backend:  ibmq_belem\n"
+            "backend menos ocupado:  ibmq_belem\n"
           ]
         }
       ],
       "source": [
-        "# Load our saved IBMQ accounts and get the least busy backend device with greater than or equal to (n+1) qubits\n",
+        "# Cargar nuestras cuentas IBMQ guardadas y obtener el dispositivo backend menos ocupado con más o igual a (n+1) qubits\n",
         "IBMQ.load_account()\n",
         "provider = IBMQ.get_provider(hub='ibm-q')\n",
         "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= (n+1) and\n",
         "                                   not x.configuration().simulator and x.status().operational==True))\n",
-        "print(\"least busy backend: \", backend)"
+        "print(\"backend menos ocupado: \", backend)"
       ]
     },
     {
@@ -979,7 +961,12 @@
         }
       ],
       "source": [
-
+        "# Ejecutar nuestro circuito en el backend menos ocupado. Supervisar la ejecución del trabajo (job) en la fila\n",
+        "from qiskit.tools.monitor import job_monitor\n",
+        "\n",
+        "transpiled_dj_circuit = transpile(dj_circuit, backend, optimization_level=3)\n",
+        "job = backend.run(transpiled_dj_circuit)\n",
+        "job_monitor(job, interval=2)"
       ]
     },
     {
@@ -988,8 +975,7 @@
       "metadata": {
         "tags": [
           "uses-hardware"
-        ],
-        "id": "gl_RyV9hD60vD"
+        ]
       },
       "outputs": [
         {
@@ -1008,7 +994,7 @@
         }
       ],
       "source": [
-        "# Get the results of the computation\n",
+        "# Obtener los resultados del cálculo\n",
         "results = job.result()\n",
         "answer = results.get_counts()\n",
         "\n",
@@ -1026,14 +1012,13 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_w9ipMJQDPZ"
       },
       "source": [
-        "## 6. Problems <a id='problems'></a>\n",
+        "## 6. Problemas <a id=\"problems\"></a>\n",
         "\n",
-        "1. Are you able to create a balanced or constant oracle of a different form?\n",
+        "1. ¿Eres capaz de crear un oráculo balanceado o constante de una forma diferente?\n",
         "\n",
-        "2. The function `dj_problem_oracle` (below) returns a Deutsch-Jozsa oracle for `n = 4` in the form of a gate. The gate takes 5 qubits as input where the final qubit (`q_4`) is the output qubit (as with the example oracles above). You can get different oracles by giving `dj_problem_oracle` different integers between 1 and 5. Use the Deutsch-Jozsa algorithm to decide whether each oracle is balanced or constant (**Note:** It is highly recommended you try this example using the `aer_simulator` instead of a real device)."
+        "2. La función `dj_problem_oracle` (a continuación) devuelve un oráculo de Deutsch-Jozsa para `n = 4` en forma de compuerta. La compuerta toma 5 qubits como entrada, donde el qubit final (`q_4`) es el qubit de salida (como en el ejemplo de los oráculos anteriores). Puedes obtener diferentes oráculos dando a `dj_problem_oracle` diferentes números enteros entre 1 y 5. Usa el algoritmo Deutsch-Jozsa para decidir si cada oráculo es balanceado o constante (**Nota:** se recomienda probar este ejemplo usando `aer_simulator` en lugar de un dispositivo real)."
       ]
     },
     {
@@ -1054,7 +1039,7 @@
       "metadata": {
       },
       "source": [
-        "## 7. References <a id=\"references\"></a>\n",
+        "## 7. Referencias <a id=\"references\"></a>\n",
         "\n",
         "1. David Deutsch and Richard Jozsa (1992). \"Rapid solutions of problems by quantum computation\". Proceedings of the Royal Society of London A. 439: 553–558.  [doi:10.1098/rspa.1992.0167](https://doi.org/10.1098%2Frspa.1992.0167).\n",
         "2. R. Cleve; A. Ekert; C. Macchiavello; M. Mosca (1998). \"Quantum algorithms revisited\". Proceedings of the Royal Society of London A. 454: 339–354. [doi:10.1098/rspa.1998.0164](https://doi.org/10.1098%2Frspa.1998.0164)."

From 472a043cce2583ac86a84663b84c6864f1a9529e Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Tue, 14 Jun 2022 13:58:41 +0200
Subject: [PATCH 55/62] added reset button

---
 .../MiniComposer/CircuitSandboxWidget.vue     | 58 ++++++++++---------
 1 file changed, 31 insertions(+), 27 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index 4155d544c..1c7af16ba 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -20,7 +20,14 @@
       <h1 class="mini-composer__circuit-section__title">
         Circuit
       </h1>
+      <button
+        class="mini-composer__circuit-section__reset"
+        @click="onResetButton"
+      >
+        Reset <PlayIcon />
+      </button>
       <Circuit
+        class="mini-composer__circuit-section__circuit-lines"
         :circuit-state="circuitState"
         :auto-measure-gate="false"
         :max-lines="circuitState.length"
@@ -58,6 +65,7 @@
 import { ref } from '@vue/reactivity'
 import { Options, Vue, prop } from 'vue-class-component'
 import draggable from 'vuedraggable'
+import PlayIcon from '@carbon/icons-vue/lib/reset/16'
 import SolutionStateIndicator from '../common/SolutionStateIndicator.vue'
 import GatesPool from './GatesPool.vue'
 import Circuit from './Circuit.vue'
@@ -75,7 +83,8 @@ class Props {
     GatesPool,
     draggable,
     SymbolicNotation,
-    SolutionStateIndicator
+    SolutionStateIndicator,
+    PlayIcon
   }
 })
 export default class CircuitSandboxWidget extends Vue.with(Props) {
@@ -154,7 +163,7 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
       })
   }
 
-  onRestartButton () {
+  onResetButton () {
     this.circuitState = [[]]
   }
 }
@@ -213,38 +222,33 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
   &__circuit-section {
     grid-area: circuit;
     padding: $spacing-05;
+    display: grid;
+    grid-template-columns: 1fr 4rem;
+    grid-template-rows: min-content 1fr;
+    grid-template-areas:
+      "title reset"
+      "line line";
+
     &__title {
+      grid-area: title;
       margin-top: $spacing-03;
       @include type-style('heading-01');
     }
-    &__qubit-line {
-      position: relative;
-      &__slot-container {
-        display: flex;
-        flex-flow: row;
-
-        position: absolute;
-        top: 0px;
-        height: 100%;
-        width: 100%;
-        align-items: center;
-        padding: 0 $spacing-07;
-      }
-      &__slot {
-        display: flex;
-        flex-flow: row;
-        flex: 1 1 auto;
-        max-width: 100%;
+    &__reset {
+      @include type-style('body-short-01');
+      grid-area: reset;
+      display: flex;
+      flex-flow: row;
+      gap: $spacing-03;
+      color: $link-color-tertiary;
 
-        &__gate {
-          margin-right: $spacing-02;
-          &.sortable-ghost {
-            transition: opacity 0.2s ease-out;
-            opacity: 0.5;
-          }
-        }
+      &:hover {
+        color: $link-hover-color-tertiary;
       }
     }
+    &__circuit-lines {
+      grid-area: line;
+    }
   }
   &__state-views {
     grid-area: lesson;

From 5465be4bd9b6b0d77ac6fe4bfc54cb391a983bf9 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Tue, 14 Jun 2022 15:05:04 +0200
Subject: [PATCH 56/62] simplified css classes

---
 .../MiniComposer/CircuitSandboxWidget.vue     | 40 +++++++++----------
 1 file changed, 19 insertions(+), 21 deletions(-)

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index 1c7af16ba..f6353fa2e 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -39,21 +39,21 @@
       class="mini-composer__explanation"
     />
     <div class="mini-composer__state-views">
-      <section class="mini-composer__state-views__view">
-        <h1 class="mini-composer__state-views__view__title">
+      <section>
+        <h1 class="mini-composer__state-views__title">
           Matrix
         </h1>
         <SymbolicNotation
-          class="mini-composer__state-views__view__area"
+          class="mini-composer__state-views__area"
           :tex="matrixTex"
         />
       </section>
-      <section class="mini-composer__state-views__view">
-        <h1 class="mini-composer__state-views__view__title">
+      <section>
+        <h1 class="mini-composer__state-views__title">
           State Vector
         </h1>
         <SymbolicNotation
-          class="mini-composer__state-views__view__area"
+          class="mini-composer__state-views__area"
           :tex="stateVectorTex"
         />
       </section>
@@ -258,22 +258,20 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
     border-left: 1px solid $border-color;
     padding: $spacing-05;
 
-    &__view {
-      &__title {
-        @include type-style('heading-01');
-        margin-top: $spacing-03;
-      }
-      &__area {
-        display: flex;
-        flex-direction: column;
-        align-items: center;
-        justify-content: center;
+    &__title {
+      @include type-style('heading-01');
+      margin-top: $spacing-03;
+    }
+    &__area {
+      display: flex;
+      flex-direction: column;
+      align-items: center;
+      justify-content: center;
 
-        height: 9rem;
-        width: 100%;
-        border: 2px solid $border-color;
-        background-color: $background-color-white;
-      }
+      height: 9rem;
+      width: 100%;
+      border: 2px solid $border-color;
+      background-color: $background-color-white;
     }
   }
 }

From a06878680ed421b1858ee9ee917690dded1d5528 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Tue, 14 Jun 2022 15:05:16 +0200
Subject: [PATCH 57/62] added cursor to dragabbles

---
 frontend/vue/components/MiniComposer/Gate.vue | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/frontend/vue/components/MiniComposer/Gate.vue b/frontend/vue/components/MiniComposer/Gate.vue
index c1f0cb905..e3f4ce594 100644
--- a/frontend/vue/components/MiniComposer/Gate.vue
+++ b/frontend/vue/components/MiniComposer/Gate.vue
@@ -118,5 +118,9 @@ export default class Gate extends Vue.with(Props) {
   &_keep {
     opacity: 0;
   }
+
+  :hover {
+    cursor: grab;
+  }
 }
 </style>

From 9f2ac5f0c71e177e9f7b6f08e49576bf2a5b61c6 Mon Sep 17 00:00:00 2001
From: Gregorio Iniesta <korgan00@gmail.com>
Date: Tue, 14 Jun 2022 15:08:16 +0200
Subject: [PATCH 58/62] fixed borders on mobile

---
 .../vue/components/MiniComposer/CircuitSandboxWidget.vue     | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
index f6353fa2e..749a02655 100644
--- a/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -258,6 +258,11 @@ export default class CircuitSandboxWidget extends Vue.with(Props) {
     border-left: 1px solid $border-color;
     padding: $spacing-05;
 
+    @include mq ($until: medium) {
+      border-left: none;
+      border-top: 1px solid $border-color;
+    }
+
     &__title {
       @include type-style('heading-01');
       margin-top: $spacing-03;

From 412916e1863a793f9a1fc26e0e614490b785fda8 Mon Sep 17 00:00:00 2001
From: Claudia Zendejas-Morales <clausia@ciencias.unam.mx>
Date: Tue, 14 Jun 2022 16:04:15 +0000
Subject: [PATCH 59/62] Translate machine-learning-qiskit-pytorch.ipynb via
 GitLocalize

---
 .../machine-learning-qiskit-pytorch.ipynb     | 748 ++++++++++++++++++
 1 file changed, 748 insertions(+)
 create mode 100644 translations/es/ch-machine-learning/machine-learning-qiskit-pytorch.ipynb

diff --git a/translations/es/ch-machine-learning/machine-learning-qiskit-pytorch.ipynb b/translations/es/ch-machine-learning/machine-learning-qiskit-pytorch.ipynb
new file mode 100644
index 000000000..dc0e4bfed
--- /dev/null
+++ b/translations/es/ch-machine-learning/machine-learning-qiskit-pytorch.ipynb
@@ -0,0 +1,748 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "tags": [
+          "remove_cell"
+        ]
+      },
+      "source": [
+        "# Redes Neuronales Híbridas cuánticas-clásicas con PyTorch y Qiskit"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "El aprendizaje automático (machine learnng, ML) se ha establecido como un campo interdisciplinario exitoso que busca extraer matemáticamente información generalizable de los datos. Incluirlo en la computación cuántica da lugar a interesantes áreas de investigación que buscan aprovechar los principios de la mecánica cuántica para aumentar el aprendizaje automático o viceversa. Ya sea que su objetivo sea mejorar los algoritmos de ML clásicos dejando los cálculos difíciles a una computadora cuántica u optimizar algoritmos cuánticos usando arquitecturas de ML clásicas, ambos se encuentran bajo el marco diverso del aprendizaje automático cuántico (quantum machine learning, QML).\n",
+        "\n",
+        "En este capítulo, exploramos cómo una red neuronal clásica se puede modificar parcialmente para crear una red neuronal cuántica-clásica híbrida. Codificaremos un ejemplo sencillo que integra **Qiskit** con un paquete de software de código abierto de última generación: **[PyTorch](https://pytorch.org/)**. El propósito de este ejemplo es demostrar la facilidad de integrar Qiskit con las herramientas de ML existentes y alentar a los profesionales de ML a explorar lo que es posible con la computación cuántica.\n",
+        "\n",
+        "## Contents\n",
+        "\n",
+        "1. [¿Cómo Funciona?](#how)<br> 1.1 [Preliminares](#prelims)\n",
+        "2. [Entonces, ¿Cómo entra en Escena lo Cuántico?](#quantumlayer)\n",
+        "3. [¡Programemos!](#code)<br> 3.1 [Importaciones](#imports)<br> 3.2 [Crea una \"Clase Cuántica\" con Qiskit](#q-class)<br> 3.3 [Crea una \"Clase Cuántica-Clásica\" con PyTorch](#qc-class)<br> 3.4 [Carga y Preprocesamiento de Datos](#data-loading-preprocessing)<br> 3.5 [Creación de la Red Neuronal Híbrida](#hybrid-nn)<br> 3.6 [Entrenamiento de la Red](#training)<br> 3.7 [Probar la Red](#testing)\n",
+        "4. [¿Qué Sigue?](#what-now)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 1. ¿Cómo funciona? <a id=\"how\"></a>\n",
+        "\n",
+        "<img src=\"hybridnetwork.png\">\n",
+        "\n",
+        "La **Figura 1** ilustra el marco que construiremos en este capítulo. En última instancia, crearemos una red neuronal cuántica-clásica híbrida que busca clasificar dígitos dibujados a mano. Ten en cuenta que las conexiones que se muestran en esta imagen están todas dirigidas hacia abajo; sin embargo, la direccionalidad no se indica visualmente. "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 1.1 Preliminares <a id=\"prelims\"></a>\n",
+        "\n",
+        "Los antecedentes presentados aquí sobre las redes neuronales clásicas se incluyen para establecer ideas relevantes y terminología compartida; sin embargo, siguen siendo de un nivel extremadamente alto. **Si deseas profundizar un poco más en las redes neuronales clásicas, mira la serie de videos bien hechos del youtuber** [3Blue1Brown](https://youtu.be/aircAruvnKk). Como alternativa, si ya estás familiarizado con las redes clásicas, puedes [pasar a la siguiente sección](#quantumlayer).\n",
+        "\n",
+        "###### Neurons and Weights\n",
+        "\n",
+        "Una red neuronal es, en última instancia, solo una función elaborada que se construye al componer bloques de construcción más pequeños llamados neuronas. Una ***neurona*** suele ser una función simple, fácil de calcular y no lineal que mapea una o más entradas a un único número real. La salida única de una neurona generalmente se copia y se alimenta como entrada a otras neuronas. Gráficamente, representamos las neuronas como nodos en un grafo y dibujamos conexiones dirigidas entre los nodos para indicar que se usará la salida de una neurona como entrada para otras neuronas. También es importante tener en cuenta que cada arista de nuestro grafo suele estar asociada con un valor escalar llamado [***peso***](https://en.wikipedia.org/wiki/Artificial_neural_network#Connections_and_weights). La idea aquí es que cada una de las entradas a una neurona se multiplique por un escalar diferente antes de recopilarse y procesarse en un solo valor. El objetivo al entrenar una red neuronal consiste principalmente en elegir nuestros pesos para que la red se comporte de una manera particular.\n",
+        "\n",
+        "###### Redes Neuronales Prealimentadas\n",
+        "\n",
+        "También vale la pena señalar que el tipo particular de red neuronal del que nos ocuparemos se denomina **[red neuronal prealimentada (feed-forward neural network, FFNN)](https://en.wikipedia.org/wiki/Feedforward_neural_network)**. Esto significa que a medida que los datos fluyen a través de nuestra red neuronal, nunca volverán a una neurona que ya visitó. De manera equivalente, podrías decir que el grafo que describe nuestra red neuronal es un **[grafo acíclico dirigido (directed acyclic graph, DAG)](https://en.wikipedia.org/wiki/Directed_acyclic_graph)**. Además, estipularemos que las neuronas dentro de la misma capa de nuestra red neuronal no tendrán conexiones entre ellas.\n",
+        "\n",
+        "###### Estructura de Entrada y Salida de las Capas\n",
+        "\n",
+        "La entrada a una red neuronal es un vector clásico (de valor real). Cada componente del vector de entrada se multiplica por un peso diferente y se alimenta a una capa de neuronas de acuerdo con la estructura del grafo de la red. Después de evaluar cada neurona de la capa, los resultados se recopilan en un nuevo vector donde el i-ésimo componente registra la salida de la i-ésima neurona. Este nuevo vector se puede tratar como una entrada para una nueva capa, y así sucesivamente. Usaremos el término estándar ***capa oculta*** para describir todas las capas de nuestra red, excepto la primera y la última.\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 2. Entonces, ¿Cómo entra en Escena lo Cuántico? <a id=\"quantumlayer\"> </a>\n",
+        "\n",
+        "Para crear una red neuronal cuántica-clásica, uno puede implementar una capa oculta para nuestra red neuronal utilizando un circuito cuántico parametrizado. Por \"circuito cuántico parametrizado\", nos referimos a un circuito cuántico donde los ángulos de rotación para cada compuerta están especificados por los componentes de un vector de entrada clásico. Las salidas de la capa anterior de nuestra red neuronal se recopilarán y usarán como entradas para nuestro circuito parametrizado. Las mediciones estadísticas de nuestro circuito cuántico se pueden recopilar y utilizar como entradas para la siguiente capa. A continuación se muestra un simple ejemplo:\n",
+        "\n",
+        "<img src=\"neuralnetworkQC.png\">\n",
+        "\n",
+        "Aquí, $\\sigma$ es una [función no lineal](https://en.wikipedia.org/wiki/Activation_function) y $h_i$ es el valor de la neurona $i$ en cada capa oculta. $R(h_i)$ representa cualquier compuerta de rotación sobre un ángulo igual a $h_i$ e $y$ es el valor de predicción final generado a partir de la red híbrida.\n",
+        "\n",
+        "### ¿Qué pasa con la retropropagación?\n",
+        "\n",
+        "Si estás familiarizado con el ML clásico, es posible que te preguntes de inmediato *¿cómo calculamos los gradientes cuando se trata de circuitos cuánticos?* Esto sería necesario para incorporar potentes técnicas de optimización como el **[descenso de gradiente](https://en.wikipedia.org/wiki/Gradient_descent)**. Se vuelve un poco técnico, pero en resumen, podemos ver un circuito cuántico como una caja negra y el gradiente de esta caja negra con respecto a sus parámetros se puede calcular de la siguiente manera:\n",
+        "\n",
+        "\n",
+        "<img src=\"quantumgradient.png\">\n",
+        "\n",
+        "donde $\\theta$ representa los parámetros del circuito cuántico y $s$ es un cambio macroscópico. El gradiente es entonces simplemente la diferencia entre nuestro circuito cuántico evaluado en $\\theta+s$ y $\\theta - s$. Por lo tanto, podemos diferenciar sistemáticamente nuestro circuito cuántico como parte de una rutina de retropropagación más grande. Esta regla de forma cerrada para calcular el gradiente de los parámetros del circuito cuántico se conoce como **[regla de cambio de parámetros](https://arxiv.org/pdf/1905.13311.pdf)**. "
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 2,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "# instalar los paquetes necesarios para esta página específica\n",
+        "!pip install torchvision"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 3. Let's code! <a id=\"code\"></a>\n",
+        "\n",
+        "### 3.1 Importaciones <a id=\"imports\"></a>\n",
+        "\n",
+        "Primero, importamos algunos paquetes útiles que necesitaremos, incluyendo Qiskit y PyTorch."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 1,
+      "metadata": {
+        "id": "gl_dbuECuH3Og"
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "import numpy as np\n",
+        "import matplotlib.pyplot as plt\n",
+        "\n",
+        "import torch\n",
+        "from torch.autograd import Function\n",
+        "from torchvision import datasets, transforms\n",
+        "import torch.optim as optim\n",
+        "import torch.nn as nn\n",
+        "import torch.nn.functional as F\n",
+        "\n",
+        "import qiskit\n",
+        "from qiskit import transpile, assemble\n",
+        "from qiskit.visualization import *"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 3.2 Crea una \"Clase Cuántica\" con Qiskit <a id=\"q-class\"></a>\n",
+        "\n",
+        "Convenientemente, podemos poner nuestras funciones cuánticas de Qiskit en una clase. Primero, especificamos cuántos parámetros cuánticos entrenables y cuántas iteraciones deseamos usar en nuestro circuito cuántico. En este ejemplo, lo mantendremos simple y utilizaremos un circuito de 1 qubit con un parámetro cuántico entrenable $\\theta$. Codificamos de forma fija el circuito por simplicidad y empleamos una rotación $RY$ con el ángulo $\\theta$ para entrenar la salida de nuestro circuito. El circuito se ve así:\n",
+        "\n",
+        "<img src=\"https://gitlocalize.com/repo/7494/es/notebooks/ch-machine-learning/hybridnetwork.png\" class=\"\">\n",
+        "\n",
+        "Para medir la salida en la base $z$, calculamos el valor esperado de $\\sigma_\\mathbf{z}$. $$\\sigma_\\mathbf{z} = \\sum_i z_i p(z_i)$$ Más adelante veremos cómo todo esto se relaciona con la red neuronal híbrida."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 6,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "class QuantumCircuit:\n",
+        "    \"\"\" \n",
+        "    Esta clase proporciona una interfaz simple para la interacción\n",
+        "    con el circuito cuántico\n",
+        "    \"\"\"\n",
+        "    \n",
+        "    def __init__(self, n_qubits, backend, shots):\n",
+        "        # --- Definición de circuito ---\n",
+        "        self._circuit = qiskit.QuantumCircuit(n_qubits)\n",
+        "        \n",
+        "        all_qubits = [i for i in range(n_qubits)]\n",
+        "        self.theta = qiskit.circuit.Parameter('theta')\n",
+        "        \n",
+        "        self._circuit.h(all_qubits)\n",
+        "        self._circuit.barrier()\n",
+        "        self._circuit.ry(self.theta, all_qubits)\n",
+        "        \n",
+        "        self._circuit.measure_all()\n",
+        "        # ---------------------------\n",
+        "\n",
+        "        self.backend = backend\n",
+        "        self.shots = shots\n",
+        "    \n",
+        "    def run(self, thetas):\n",
+        "        t_qc = transpile(self._circuit,\n",
+        "                         self.backend)\n",
+        "        qobj = assemble(t_qc,\n",
+        "                        shots=self.shots,\n",
+        "                        parameter_binds = [{self.theta: theta} for theta in thetas])\n",
+        "        job = self.backend.run(qobj)\n",
+        "        result = job.result().get_counts()\n",
+        "        \n",
+        "        counts = np.array(list(result.values()))\n",
+        "        states = np.array(list(result.keys())).astype(float)\n",
+        "        \n",
+        "        # Calcular probabilidades para cada estado\n",
+        "        probabilities = counts / self.shots\n",
+        "        # Obtener el valor esperado del estado\n",
+        "        expectation = np.sum(states * probabilities)\n",
+        "        \n",
+        "        return np.array([expectation])"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_XKfoMQcXtW"
+      },
+      "source": [
+        "Let's test the implementation"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 3,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Valor esperado para la rotación pi 0.57\n"
+          ]
+        },
+        {
+          "data": {
+            "image/svg+xml": [
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+            ],
+            "text/plain": [
+              "<Figure size 417.879x144.48 with 1 Axes>"
+            ]
+          },
+          "execution_count": 3,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "simulator = qiskit.Aer.get_backend('aer_simulator')\n",
+        "\n",
+        "circuit = QuantumCircuit(1, simulator, 100)\n",
+        "print('Valor esperado para la rotación pi {}'.format(circuit.run([np.pi])[0]))\n",
+        "circuit._circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 3.3 Crea una \"Clase Cuántica-Clásica\" con PyTorch <a id=\"qc-class\"></a>\n",
+        "\n",
+        "Now that our quantum circuit is defined, we can create the functions needed for backpropagation using PyTorch. [The forward and backward passes](http://www.ai.mit.edu/courses/6.034b/backprops.pdf) contain elements from our Qiskit class. The backward pass directly computes the analytical gradients using the finite difference formula we introduced above."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 8,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "class HybridFunction(Function):\n",
+        "    \"\"\" Cuántico híbrido - definición de función clásica \"\"\"\n",
+        "    \n",
+        "    @staticmethod\n",
+        "    def forward(ctx, input, quantum_circuit, shift):\n",
+        "        \"\"\" Cálculo de pase hacia adelante \"\"\"\n",
+        "        ctx.shift = shift\n",
+        "        ctx.quantum_circuit = quantum_circuit\n",
+        "\n",
+        "        expectation_z = ctx.quantum_circuit.run(input[0].tolist())\n",
+        "        result = torch.tensor([expectation_z])\n",
+        "        ctx.save_for_backward(input, result)\n",
+        "\n",
+        "        return result\n",
+        "        \n",
+        "    @staticmethod\n",
+        "    def backward(ctx, grad_output):\n",
+        "        \"\"\" Cálculo de pase hacia atrás \"\"\"\n",
+        "        input, expectation_z = ctx.saved_tensors\n",
+        "        input_list = np.array(input.tolist())\n",
+        "        \n",
+        "        shift_right = input_list + np.ones(input_list.shape) * ctx.shift\n",
+        "        shift_left = input_list - np.ones(input_list.shape) * ctx.shift\n",
+        "        \n",
+        "        gradients = []\n",
+        "        for i in range(len(input_list)):\n",
+        "            expectation_right = ctx.quantum_circuit.run(shift_right[i])\n",
+        "            expectation_left  = ctx.quantum_circuit.run(shift_left[i])\n",
+        "            \n",
+        "            gradient = torch.tensor([expectation_right]) - torch.tensor([expectation_left])\n",
+        "            gradients.append(gradient)\n",
+        "        gradients = np.array([gradients]).T\n",
+        "        return torch.tensor([gradients]).float() * grad_output.float(), None, None\n",
+        "\n",
+        "class Hybrid(nn.Module):\n",
+        "    \"\"\" Cuántico híbrido - definición de capa clásica \"\"\"\n",
+        "    \n",
+        "    def __init__(self, backend, shots, shift):\n",
+        "        super(Hybrid, self).__init__()\n",
+        "        self.quantum_circuit = QuantumCircuit(1, backend, shots)\n",
+        "        self.shift = shift\n",
+        "        \n",
+        "    def forward(self, input):\n",
+        "        return HybridFunction.apply(input, self.quantum_circuit, self.shift)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 3.4 Carga y Preprocesamiento de Datos <a id=\"data-loading-preprocessing\"></a>\n",
+        "\n",
+        "##### Uniendo todo:\n",
+        "\n",
+        "Crearemos una red neuronal híbrida simple para clasificar imágenes de dos tipos de dígitos (0 o 1) del conjunto de [datos MNIST](http://yann.lecun.com/exdb/mnist/). Primero cargamos la base de datos MNIST y filtramos las imágenes que contienen 0 y 1. Estos servirán como entradas para que nuestra red neuronal los clasifique."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "id": "gl_8zlW0LLDLO"
+      },
+      "source": [
+        "#### Training data"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 9,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "# Concentrándose en las primeras 100 muestras\n",
+        "n_samples = 100\n",
+        "\n",
+        "X_train = datasets.MNIST(root='./data', train=True, download=True,\n",
+        "                         transform=transforms.Compose([transforms.ToTensor()]))\n",
+        "\n",
+        "# Dejando solo las etiquetas 0 y 1\n",
+        "idx = np.append(np.where(X_train.targets == 0)[0][:n_samples], \n",
+        "                np.where(X_train.targets == 1)[0][:n_samples])\n",
+        "\n",
+        "X_train.data = X_train.data[idx]\n",
+        "X_train.targets = X_train.targets[idx]\n",
+        "\n",
+        "train_loader = torch.utils.data.DataLoader(X_train, batch_size=1, shuffle=True)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 6,
+      "metadata": {
+        "id": "gl_ahUhS7NzMT"
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 720x216 with 6 Axes>"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "n_samples_show = 6\n",
+        "\n",
+        "data_iter = iter(train_loader)\n",
+        "fig, axes = plt.subplots(nrows=1, ncols=n_samples_show, figsize=(10, 3))\n",
+        "\n",
+        "while n_samples_show > 0:\n",
+        "    images, targets = data_iter.__next__()\n",
+        "\n",
+        "    axes[n_samples_show - 1].imshow(images[0].numpy().squeeze(), cmap='gray')\n",
+        "    axes[n_samples_show - 1].set_xticks([])\n",
+        "    axes[n_samples_show - 1].set_yticks([])\n",
+        "    axes[n_samples_show - 1].set_title(\"Labeled: {}\".format(targets.item()))\n",
+        "    \n",
+        "    n_samples_show -= 1"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "#### Datos de prueba"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 11,
+      "metadata": {
+        "id": "gl_TEQ0E2yNqr"
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "n_samples = 50\n",
+        "\n",
+        "X_test = datasets.MNIST(root='./data', train=False, download=True,\n",
+        "                        transform=transforms.Compose([transforms.ToTensor()]))\n",
+        "\n",
+        "idx = np.append(np.where(X_test.targets == 0)[0][:n_samples], \n",
+        "                np.where(X_test.targets == 1)[0][:n_samples])\n",
+        "\n",
+        "X_test.data = X_test.data[idx]\n",
+        "X_test.targets = X_test.targets[idx]\n",
+        "\n",
+        "test_loader = torch.utils.data.DataLoader(X_test, batch_size=1, shuffle=True)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Hasta ahora, hemos cargado los datos y codificado una clase que crea nuestro circuito cuántico que contiene 1 parámetro entrenable. Este parámetro cuántico se insertará en una red neuronal clásica junto con los otros parámetros clásicos para formar la red neuronal híbrida. También creamos funciones de pase hacia atrás y hacia adelante que nos permiten hacer retropropagación y optimizar nuestra red neuronal. Por último, debemos especificar nuestra arquitectura de red neuronal, de modo que podamos comenzar a entrenar nuestros parámetros utilizando técnicas de optimización proporcionadas por PyTorch.\n",
+        "\n",
+        "### 3.5 Creación de la Red Neuronal Híbrida <a id=\"hybrid-nn\"></a>\n",
+        "\n",
+        "Podemos usar una canalización (pipeline) ordenada de PyTorch para crear una arquitectura de red neuronal. La red deberá ser compatible en términos de su dimensionalidad cuando insertemos la capa cuántica (es decir, nuestro circuito cuántico). Dado que lo cuántico en este ejemplo contiene 1 parámetro, debemos asegurarnos de que la red condense las neuronas reduciendo al tamaño 1. Creamos una red neuronal convolucional típica con dos capas completamente conectadas al final. El valor de la última neurona de la capa totalmente conectada se introduce como parámetro $\\theta$ en nuestro circuito cuántico. La medición del circuito luego sirve como la predicción final para 0 o 1 según lo proporcionado por una medición $\\sigma_z$."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 12,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "class Net(nn.Module):\n",
+        "    def __init__(self):\n",
+        "        super(Net, self).__init__()\n",
+        "        self.conv1 = nn.Conv2d(1, 6, kernel_size=5)\n",
+        "        self.conv2 = nn.Conv2d(6, 16, kernel_size=5)\n",
+        "        self.dropout = nn.Dropout2d()\n",
+        "        self.fc1 = nn.Linear(256, 64)\n",
+        "        self.fc2 = nn.Linear(64, 1)\n",
+        "        self.hybrid = Hybrid(qiskit.Aer.get_backend('aer_simulator'), 100, np.pi / 2)\n",
+        "\n",
+        "    def forward(self, x):\n",
+        "        x = F.relu(self.conv1(x))\n",
+        "        x = F.max_pool2d(x, 2)\n",
+        "        x = F.relu(self.conv2(x))\n",
+        "        x = F.max_pool2d(x, 2)\n",
+        "        x = self.dropout(x)\n",
+        "        x = x.view(1, -1)\n",
+        "        x = F.relu(self.fc1(x))\n",
+        "        x = self.fc2(x)\n",
+        "        x = self.hybrid(x)\n",
+        "        return torch.cat((x, 1 - x), -1)\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 3.6 Training the Network <a id=\"training\"></a>\n",
+        "\n",
+        "¡Ya tenemos todos los ingredientes para entrenar nuestra red híbrida! Podemos especificar cualquier [optimizador de PyTorch](https://pytorch.org/docs/stable/optim.html), [tasa de aprendizaje](https://en.wikipedia.org/wiki/Learning_rate) y [función de costo/pérdida](https://en.wikipedia.org/wiki/Loss_function) para entrenar con múltiples épocas. En este caso, usamos el [optimizador Adam](https://arxiv.org/abs/1412.6980), una tasa de aprendizaje de 0.001 y la [función de pérdida de verosimilitud logarítmica negativa](https://pytorch.org/docs/stable/_modules/torch/nn/modules/loss.html)."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 9,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "name": "stderr",
+          "output_type": "stream",
+          "text": [
+            "/usr/local/anaconda3/lib/python3.7/site-packages/ipykernel_launcher.py:32: FutureWarning: The input object of type 'Tensor' is an array-like implementing one of the corresponding protocols (`__array__`, `__array_interface__` or `__array_struct__`); but not a sequence (or 0-D). In the future, this object will be coerced as if it was first converted using `np.array(obj)`. To retain the old behaviour, you have to either modify the type 'Tensor', or assign to an empty array created with `np.empty(correct_shape, dtype=object)`.\n"
+          ]
+        },
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Training [5%]\tLoss: -0.7741\n",
+            "Training [10%]\tLoss: -0.9155\n",
+            "Training [15%]\tLoss: -0.9489\n",
+            "Training [20%]\tLoss: -0.9400\n",
+            "Training [25%]\tLoss: -0.9496\n",
+            "Training [30%]\tLoss: -0.9561\n",
+            "Training [35%]\tLoss: -0.9627\n",
+            "Training [40%]\tLoss: -0.9499\n",
+            "Training [45%]\tLoss: -0.9664\n",
+            "Training [50%]\tLoss: -0.9676\n",
+            "Training [55%]\tLoss: -0.9761\n",
+            "Training [60%]\tLoss: -0.9790\n",
+            "Training [65%]\tLoss: -0.9846\n",
+            "Training [70%]\tLoss: -0.9836\n",
+            "Training [75%]\tLoss: -0.9857\n",
+            "Training [80%]\tLoss: -0.9877\n",
+            "Training [85%]\tLoss: -0.9895\n",
+            "Training [90%]\tLoss: -0.9912\n",
+            "Training [95%]\tLoss: -0.9936\n",
+            "Training [100%]\tLoss: -0.9901\n"
+          ]
+        }
+      ],
+      "source": [
+        "model = Net()\n",
+        "optimizer = optim.Adam(model.parameters(), lr=0.001)\n",
+        "loss_func = nn.NLLLoss()\n",
+        "\n",
+        "epochs = 20\n",
+        "loss_list = []\n",
+        "\n",
+        "model.train()\n",
+        "for epoch in range(epochs):\n",
+        "    total_loss = []\n",
+        "    for batch_idx, (data, target) in enumerate(train_loader):\n",
+        "        optimizer.zero_grad()\n",
+        "        # Pase hacia adelante\n",
+        "        output = model(data)\n",
+        "        # Calcular la pérdida\n",
+        "        loss = loss_func(output, target)\n",
+        "        # Pase hacia atrás\n",
+        "        loss.backward()\n",
+        "        # Optimizar los pesos\n",
+        "        optimizer.step()\n",
+        "        \n",
+        "        total_loss.append(loss.item())\n",
+        "    loss_list.append(sum(total_loss)/len(total_loss))\n",
+        "    print('Training [{:.0f}%]\\tLoss: {:.4f}'.format(\n",
+        "        100. * (epoch + 1) / epochs, loss_list[-1]))"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Mostrar el grafo de entrenamiento"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 14,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "text/plain": [
+              "Text(0, 0.5, 'Neg Log Likelihood Loss')"
+            ]
+          },
+          "execution_count": 10,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        },
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 432x288 with 1 Axes>"
+            ]
+          },
+          "metadata": {
+            "needs_background": "light"
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "plt.plot(loss_list)\n",
+        "plt.title('Convergencia de Entrenamiento de la NN Híbrida')\n",
+        "plt.xlabel('Iteraciones de Entrenamiento')\n",
+        "plt.ylabel('Pérdida de Verosimilitud Logarítmica Negativa')"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 3.7 Probar la Red <a id=\"testing\"></a>"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 15,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Rendimiento en datos de prueba:\n",
+            "\tPérdida: -0.9827\n",
+            "\tPrecisión: 100.0%\n"
+          ]
+        }
+      ],
+      "source": [
+        "model.eval()\n",
+        "with torch.no_grad():\n",
+        "    \n",
+        "    correct = 0\n",
+        "    for batch_idx, (data, target) in enumerate(test_loader):\n",
+        "        output = model(data)\n",
+        "        \n",
+        "        pred = output.argmax(dim=1, keepdim=True) \n",
+        "        correct += pred.eq(target.view_as(pred)).sum().item()\n",
+        "        \n",
+        "        loss = loss_func(output, target)\n",
+        "        total_loss.append(loss.item())\n",
+        "        \n",
+        "    print('Rendimiento en datos de prueba:\\n\\tPérdida: {:.4f}\\n\\tPrecisión: {:.1f}%'.format(\n",
+        "        sum(total_loss) / len(total_loss),\n",
+        "        correct / len(test_loader) * 100)\n",
+        "        )"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 12,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 720x216 with 6 Axes>"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "n_samples_show = 6\n",
+        "count = 0\n",
+        "fig, axes = plt.subplots(nrows=1, ncols=n_samples_show, figsize=(10, 3))\n",
+        "\n",
+        "model.eval()\n",
+        "with torch.no_grad():\n",
+        "    for batch_idx, (data, target) in enumerate(test_loader):\n",
+        "        if count == n_samples_show:\n",
+        "            break\n",
+        "        output = model(data)\n",
+        "        \n",
+        "        pred = output.argmax(dim=1, keepdim=True) \n",
+        "\n",
+        "        axes[count].imshow(data[0].numpy().squeeze(), cmap='gray')\n",
+        "\n",
+        "        axes[count].set_xticks([])\n",
+        "        axes[count].set_yticks([])\n",
+        "        axes[count].set_title('Predicho {}'.format(pred.item()))\n",
+        "        \n",
+        "        count += 1"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 4. ¿Qué Sigue? <a id=\"what-now\"></a>\n",
+        "\n",
+        "#### Si bien es totalmente posible crear redes neuronales híbridas, ¿realmente tiene algún beneficio?\n",
+        "\n",
+        "De hecho, las capas clásicas de esta red se entrenan perfectamente bien (de hecho, mejor) sin la capa cuántica. Además, es posible que hayas notado que la capa cuántica que entrenamos aquí **no genera entrelazamiento** y, por lo tanto, seguirá siendo clásicamente simulable a medida que ampliemos esta arquitectura en particular. Esto significa que si esperas lograr una ventaja cuántica utilizando redes neuronales híbridas, deberás comenzar extendiendo este código para incluir una capa cuántica más sofisticada.\n",
+        "\n",
+        "El objetivo de este ejercicio era hacerte pensar en la integración de técnicas de ML y computación cuántica para investigar si realmente hay algún elemento de interés, y gracias a PyTorch y Qiskit, esto se vuelve un poco más fácil."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 13,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
+            "text/html": [
+              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td>Qiskit</td><td>0.27.0</td></tr><tr><td>Terra</td><td>0.17.4</td></tr><tr><td>Aer</td><td>0.8.2</td></tr><tr><td>Ignis</td><td>0.6.0</td></tr><tr><td>Aqua</td><td>0.9.2</td></tr><tr><td>IBM Q Provider</td><td>0.14.0</td></tr><tr><th>System information</th></tr><tr><td>Python</td><td>3.7.7 (default, May  6 2020, 04:59:01) \n",
+              "[Clang 4.0.1 (tags/RELEASE_401/final)]</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>32.0</td></tr><tr><td colspan='2'>Thu Jun 17 15:17:23 2021 BST</td></tr></table>"
+            ],
+            "text/plain": [
+              "<IPython.core.display.HTML object>"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "import qiskit.tools.jupyter\n",
+        "%qiskit_version_table"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 2
+}

From ed26b209b073228b9fbb7528bc47c76dc98dd205 Mon Sep 17 00:00:00 2001
From: Miguel-Santos Luparelli-Mathieu <msluparelli@gmail.com>
Date: Tue, 14 Jun 2022 16:04:16 +0000
Subject: [PATCH 60/62] Translate machine-learning-qiskit-pytorch.ipynb via
 GitLocalize

---
 .../machine-learning-qiskit-pytorch.ipynb     | 22 +++++++------------
 1 file changed, 8 insertions(+), 14 deletions(-)

diff --git a/translations/es/ch-machine-learning/machine-learning-qiskit-pytorch.ipynb b/translations/es/ch-machine-learning/machine-learning-qiskit-pytorch.ipynb
index dc0e4bfed..e833f7c6c 100644
--- a/translations/es/ch-machine-learning/machine-learning-qiskit-pytorch.ipynb
+++ b/translations/es/ch-machine-learning/machine-learning-qiskit-pytorch.ipynb
@@ -20,7 +20,7 @@
         "\n",
         "En este capítulo, exploramos cómo una red neuronal clásica se puede modificar parcialmente para crear una red neuronal cuántica-clásica híbrida. Codificaremos un ejemplo sencillo que integra **Qiskit** con un paquete de software de código abierto de última generación: **[PyTorch](https://pytorch.org/)**. El propósito de este ejemplo es demostrar la facilidad de integrar Qiskit con las herramientas de ML existentes y alentar a los profesionales de ML a explorar lo que es posible con la computación cuántica.\n",
         "\n",
-        "## Contents\n",
+        "## Contenido\n",
         "\n",
         "1. [¿Cómo Funciona?](#how)<br> 1.1 [Preliminares](#prelims)\n",
         "2. [Entonces, ¿Cómo entra en Escena lo Cuántico?](#quantumlayer)\n",
@@ -49,7 +49,7 @@
         "\n",
         "Los antecedentes presentados aquí sobre las redes neuronales clásicas se incluyen para establecer ideas relevantes y terminología compartida; sin embargo, siguen siendo de un nivel extremadamente alto. **Si deseas profundizar un poco más en las redes neuronales clásicas, mira la serie de videos bien hechos del youtuber** [3Blue1Brown](https://youtu.be/aircAruvnKk). Como alternativa, si ya estás familiarizado con las redes clásicas, puedes [pasar a la siguiente sección](#quantumlayer).\n",
         "\n",
-        "###### Neurons and Weights\n",
+        "###### Neuronas y Pesos\n",
         "\n",
         "Una red neuronal es, en última instancia, solo una función elaborada que se construye al componer bloques de construcción más pequeños llamados neuronas. Una ***neurona*** suele ser una función simple, fácil de calcular y no lineal que mapea una o más entradas a un único número real. La salida única de una neurona generalmente se copia y se alimenta como entrada a otras neuronas. Gráficamente, representamos las neuronas como nodos en un grafo y dibujamos conexiones dirigidas entre los nodos para indicar que se usará la salida de una neurona como entrada para otras neuronas. También es importante tener en cuenta que cada arista de nuestro grafo suele estar asociada con un valor escalar llamado [***peso***](https://en.wikipedia.org/wiki/Artificial_neural_network#Connections_and_weights). La idea aquí es que cada una de las entradas a una neurona se multiplique por un escalar diferente antes de recopilarse y procesarse en un solo valor. El objetivo al entrenar una red neuronal consiste principalmente en elegir nuestros pesos para que la red se comporte de una manera particular.\n",
         "\n",
@@ -79,8 +79,7 @@
         "\n",
         "Si estás familiarizado con el ML clásico, es posible que te preguntes de inmediato *¿cómo calculamos los gradientes cuando se trata de circuitos cuánticos?* Esto sería necesario para incorporar potentes técnicas de optimización como el **[descenso de gradiente](https://en.wikipedia.org/wiki/Gradient_descent)**. Se vuelve un poco técnico, pero en resumen, podemos ver un circuito cuántico como una caja negra y el gradiente de esta caja negra con respecto a sus parámetros se puede calcular de la siguiente manera:\n",
         "\n",
-        "\n",
-        "<img src=\"quantumgradient.png\">\n",
+        "<img src=\"https://github.com/Qiskit/platypus/blob/main/translations/es/ch-machine-learning/quantumgradient.png?raw=true\" class=\"\">\n",
         "\n",
         "donde $\\theta$ representa los parámetros del circuito cuántico y $s$ es un cambio macroscópico. El gradiente es entonces simplemente la diferencia entre nuestro circuito cuántico evaluado en $\\theta+s$ y $\\theta - s$. Por lo tanto, podemos diferenciar sistemáticamente nuestro circuito cuántico como parte de una rutina de retropropagación más grande. Esta regla de forma cerrada para calcular el gradiente de los parámetros del circuito cuántico se conoce como **[regla de cambio de parámetros](https://arxiv.org/pdf/1905.13311.pdf)**. "
       ]
@@ -103,7 +102,7 @@
       "metadata": {
       },
       "source": [
-        "## 3. Let's code! <a id=\"code\"></a>\n",
+        "## 3. ¡Programemos! <a id=\"code\"></a>\n",
         "\n",
         "### 3.1 Importaciones <a id=\"imports\"></a>\n",
         "\n",
@@ -114,7 +113,6 @@
       "cell_type": "code",
       "execution_count": 1,
       "metadata": {
-        "id": "gl_dbuECuH3Og"
       },
       "outputs": [
 
@@ -204,10 +202,9 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_XKfoMQcXtW"
       },
       "source": [
-        "Let's test the implementation"
+        "Probemos la implementación"
       ]
     },
     {
@@ -253,7 +250,7 @@
       "source": [
         "### 3.3 Crea una \"Clase Cuántica-Clásica\" con PyTorch <a id=\"qc-class\"></a>\n",
         "\n",
-        "Now that our quantum circuit is defined, we can create the functions needed for backpropagation using PyTorch. [The forward and backward passes](http://www.ai.mit.edu/courses/6.034b/backprops.pdf) contain elements from our Qiskit class. The backward pass directly computes the analytical gradients using the finite difference formula we introduced above."
+        "Ahora, que nuestro circuito cuántico está definido, podemos crear las funciones necesarias para la retropropagación usando PyTorch. [Los pases hacia adelante y hacia atrás](http://www.ai.mit.edu/courses/6.034b/backprops.pdf) contienen elementos de nuestra clase Qiskit. El pase hacia atrás calcula directamente los gradientes utilizando la fórmula de diferencia finita que presentamos anteriormente."
       ]
     },
     {
@@ -326,10 +323,9 @@
     {
       "cell_type": "markdown",
       "metadata": {
-        "id": "gl_8zlW0LLDLO"
       },
       "source": [
-        "#### Training data"
+        "#### Datos de entrenamiento"
       ]
     },
     {
@@ -361,7 +357,6 @@
       "cell_type": "code",
       "execution_count": 6,
       "metadata": {
-        "id": "gl_ahUhS7NzMT"
       },
       "outputs": [
         {
@@ -407,7 +402,6 @@
       "cell_type": "code",
       "execution_count": 11,
       "metadata": {
-        "id": "gl_TEQ0E2yNqr"
       },
       "outputs": [
 
@@ -476,7 +470,7 @@
       "metadata": {
       },
       "source": [
-        "### 3.6 Training the Network <a id=\"training\"></a>\n",
+        "### 3.6 Entrenamiento de la Red <a id=\"training\"></a>\n",
         "\n",
         "¡Ya tenemos todos los ingredientes para entrenar nuestra red híbrida! Podemos especificar cualquier [optimizador de PyTorch](https://pytorch.org/docs/stable/optim.html), [tasa de aprendizaje](https://en.wikipedia.org/wiki/Learning_rate) y [función de costo/pérdida](https://en.wikipedia.org/wiki/Loss_function) para entrenar con múltiples épocas. En este caso, usamos el [optimizador Adam](https://arxiv.org/abs/1412.6980), una tasa de aprendizaje de 0.001 y la [función de pérdida de verosimilitud logarítmica negativa](https://pytorch.org/docs/stable/_modules/torch/nn/modules/loss.html)."
       ]

From 4d16c3b15de9e10a4838b9bf99522b5b004c3c87 Mon Sep 17 00:00:00 2001
From: MR-Asif12116135 <mrasif12116135@gmail.com>
Date: Tue, 14 Jun 2022 18:42:10 +0000
Subject: [PATCH 61/62] Translate deutsch-jozsa.ipynb via GitLocalize

---
 .../bn/ch-algorithms/deutsch-jozsa.ipynb      | 1103 +++++++++++++++++
 1 file changed, 1103 insertions(+)
 create mode 100644 translations/bn/ch-algorithms/deutsch-jozsa.ipynb

diff --git a/translations/bn/ch-algorithms/deutsch-jozsa.ipynb b/translations/bn/ch-algorithms/deutsch-jozsa.ipynb
new file mode 100644
index 000000000..f1dd0799b
--- /dev/null
+++ b/translations/bn/ch-algorithms/deutsch-jozsa.ipynb
@@ -0,0 +1,1103 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "tags": [
+          "remove_cell"
+        ]
+      },
+      "source": [
+        "# Deutsch-Jozsa অ্যালগরিদম"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "এই বিভাগে, আমরা প্রথমে Deutsch-Jozsa সমস্যা এবং এটি সমাধান করার জন্য ক্লাসিক্যাল এবং কোয়ান্টাম অ্যালগরিদম উপস্থাপন করি। তারপরে আমরা কিস্কিট ব্যবহার করে কোয়ান্টাম অ্যালগরিদম বাস্তবায়ন করবএবং এটি একটি সিমুলেটর এবং ডিভাইসে চালাবো।"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 1। পরিচিতি<a id=\"introduction\"></a>"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Deutsch-Jozsa অ্যালগরিদম, প্রথম রেফারেন্স [1]-এ প্রবর্তিত হয়েছিল, এটি একটি কোয়ান্টাম অ্যালগরিদমের প্রথম উদাহরণ যা সেরা ক্লাসিক্যাল অ্যালগরিদমের চেয়ে ভাল কাজ করে। এটি দেখিয়েছে যে একটি নির্দিষ্ট সমস্যার জন্য একটি কম্পিউটেশনাল টুল হিসাবে একটি কোয়ান্টাম কম্পিউটার ব্যবহার করার সুবিধা থাকতে পারে।"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 1.1 ডয়েচ-জোজসা সমস্যা<a id=\"djproblem\"> </a>\n",
+        "\n",
+        "আমাদেরকে একটি লুকানো বুলিয়ান ফাংশন $f$ দেওয়া হয়েছে, যা ইনপুট হিসাবে বিটগুলির একটি স্ট্রিং নেয় এবং $0$ বা $1$ প্রদান করে, অর্থাৎ:\n",
+        "\n",
+        "$$ f({x_0,x_1,x_2,...}) \\rightarrow 0 \\textrm{ or } 1 \\textrm{ , where } x_n \\textrm{ is } 0 \\textrm{ or } 1$$\n",
+        "\n",
+        "প্রদত্ত বুলিয়ান ফাংশনের বৈশিষ্ট্য হল এটি হয় সুষম বা ধ্রুবক হওয়ার নিশ্চয়তা। একটি ধ্রুবক ফাংশন যেকোনো ইনপুটের জন্য সমস্ত $0$'স বা সমস্ত $1$'স ফেরত দেয়, যখন একটি ভারসাম্যপূর্ণ ফাংশন সমস্ত ইনপুটের অর্ধেকের জন্য $0$' এবং বাকি অর্ধেকের জন্য $1$'স ফেরত দেয়। আমাদের কাজ হল প্রদত্ত ফাংশনটি সুষম বা ধ্রুবক কিনা তা নির্ধারণ করা।\n",
+        "\n",
+        "মনে রাখবেন যে Deutsch-Jozsa সমস্যাটি একক বিট ডয়েচ সমস্যার একটি $n$-বিট এক্সটেনশন।\n",
+        "\n",
+        "### 1.2ক্লাসিক্যাল সমাধান<a id=\"classical-solution\"> </a>\n",
+        "\n",
+        "ক্লাসিকভাবে, সর্বোত্তম ক্ষেত্রে, ওরাকলের কাছে দুটি প্রশ্ন নির্ধারণ করতে পারে যে লুকানো বুলিয়ান ফাংশন, $f(x)$, ভারসাম্যপূর্ণ কিনা: যেমন আমরা যদি $f(0,0,0,...)\\rightarrow উভয়ই পাই 0$ এবং $f(1,0,0,...) \\rightarrow 1$, তাহলে আমরা জানি যে ফাংশনটি ভারসাম্যপূর্ণ কারণ আমরা দুটি ভিন্ন আউটপুট পেয়েছি।\n",
+        "\n",
+        "সবচেয়ে খারাপ ক্ষেত্রে, যদি আমরা চেষ্টা করি প্রতিটি ইনপুটের জন্য একই আউটপুট দেখতে থাকি, তাহলে $f(x)$ ধ্রুবক রয়েছে তা নিশ্চিত করার জন্য আমাদের সম্ভাব্য সমস্ত ইনপুটের অর্ধেক এবং একটি পরীক্ষা করতে হবে। যেহেতু সম্ভাব্য ইনপুটগুলির মোট সংখ্যা হল $2^n$, এর অর্থ হল যে $2^{n-1}+1$ ট্রায়াল ইনপুট প্রয়োজন তা নিশ্চিত হতে যে $f(x)$ সবচেয়ে খারাপ ক্ষেত্রে ধ্রুবক। উদাহরণস্বরূপ, একটি $4$-বিট স্ট্রিংয়ের জন্য, যদি আমরা $16$ সম্ভাব্য সংমিশ্রণগুলির মধ্যে $8$ চেক করি, সমস্ত $0$ পেয়ে থাকি, তবুও এটি সম্ভব যে $9^\\textrm{th}$ ইনপুট একটি $1$ প্রদান করে। এবং $f(x)$ ভারসাম্যপূর্ণ। সম্ভবত, এটি একটি খুব অসম্ভাব্য ঘটনা। প্রকৃতপক্ষে, যদি আমরা ধারাবাহিকভাবে একই ফলাফল পাই, তাহলে আমরা সম্ভাব্যতা প্রকাশ করতে পারি যে ফাংশনটি $k$ ইনপুটগুলির একটি ফাংশন হিসাবে ধ্রুবক থাকে:\n",
+        "\n",
+        "$$ P_\\textrm{constant}(k) = 1 - \\frac{1}{2^{k-1}} \\qquad \\textrm{for } 1 &lt; k \\leq 2^{n-1}$$\n",
+        "\n",
+        "বাস্তবসম্মতভাবে, আমরা আমাদের ক্লাসিক্যাল অ্যালগরিদমকে প্রথম দিকে ছেঁটে ফেলতে বেছে নিতে পারি, বলুন যদি আমরা x%-এর বেশি আত্মবিশ্বাসী হতাম। কিন্তু যদি আমরা 100% আত্মবিশ্বাসী হতে চাই, তাহলে আমাদের $2^{n-1}+1$ ইনপুট চেক করতে হবে।"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 1.3 কোয়ান্টাম সমাধান<a id=\"quantum-solution\"> </a>\n",
+        "\n",
+        "একটি কোয়ান্টাম কম্পিউটার ব্যবহার করে, আমরা $f(x)$ ফাংশনে শুধুমাত্র একটি কল করার পরে 100% আত্মবিশ্বাসের সাথে এই সমস্যার সমাধান করতে পারি, তবে আমাদের কাছে $f$ ফাংশনটি কোয়ান্টাম ওরাকল হিসাবে বাস্তবায়িত আছে, যা $\\vert x রাষ্ট্রকে ম্যাপ করে। \\rangle \\vert y\\rangle $ থেকে $ \\vert x\\rangle \\vert y \\oplus f(x)\\rangle$, যেখানে $\\oplus$ যোগ মডিউল $2$। নিচে Deutsch-Jozsa অ্যালগরিদমের জন্য জেনেরিক সার্কিট দেওয়া হল।\n",
+        "\n",
+        "![image1](images/deutsch_steps.png)\n",
+        "\n",
+        "এখন, অ্যালগরিদটি ধাপে ধাপে করা যাক:\n",
+        "\n",
+        "<ol>\n",
+        "   <li>দুটি কোয়ান্টাম রেজিস্টার প্রস্তুত করুন। প্রথমটি হল একটি $n$-qubit রেজিস্টার $|0\\rangle$ এ আরম্ভ করা হয়েছে এবং দ্বিতীয়টি হল $|1\\rangle$ এ আরম্ভ করা এক-কুবিট রেজিস্টার:</li>\n",
+        "</ol>\n",
+        "\n",
+        "$$\\vert \\psi_0 \\rangle = \\vert0\\rangle^{\\otimes n} \\vert 1\\rangle$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>প্রতিটি কিউবিটে একটি হাদামার্ড গেট প্রয়োগ করুন:</li>\n",
+        "\n",
+        "\n",
+        "$$\\vert \\psi_1 \\rangle = \\frac{1}{\\sqrt{2^{n+1}}}\\sum_{x=0}^{2^n-1} \\vert x\\rangle \\left(|0\\rangle - |1 \\rangle \\right)$$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>কোয়ান্টাম ওরাকল $\\vert x\\rangle \\vert y\\rangle$ $\\vert x\\rangle \\vert y \\oplus f(x)\\rangle$: $$ \\begin{aligned} \\lvert \\psi_2 \\rangle &amp; এ প্রয়োগ করুন = frac{1}{\\sqrt{2^{n+1}}}\\sum_{x=0}^{2^n-1} \\vert x\\rangle (\\vert f(x)\\rangle - \\ vert 1 \\oplus f(x)\\rangle) \\\\ &amp; = \\frac{1}{\\sqrt{2^{n+1}}}\\sum_{x=0}^{2^n-1}(- 1)^{f(x)}|x\\rangle ( |0\\rangle - |1\\rangle ) \\end{aligned} $$</li>\n",
+        "\n",
+        "\n",
+        "যেহেতু প্রতিটি $x,f(x)$ এর জন্য হয় $0$ বা $1$।\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>এই সময়ে দ্বিতীয় একক কিউবিট রেজিস্টার উপেক্ষা করা যেতে পারে। প্রথম রেজিস্টারে প্রতিটি কিউবিটে একটি হাডামার্ড গেট প্রয়োগ করুন: $$ \\begin{aligned} \\lvert \\psi_3 \\rangle &amp; = \\frac{1}{2^n}\\sum_{x=0}^{2^n- 1}(-1)^{f(x)} \\left[ \\sum_{y=0}^{2^n-1}(-1)^{x \\cdot y} \\vert y \\rangle \\right] \\\\ &amp; = \\frac{1}{2^n}\\sum_{y=0}^{2^n-1} \\left[ \\sum_{x=0}^{2^n-1}(-1 )^{f(x)}(-1)^{x \\cdot y} \\right] \\vert y \\rangle \\end{aligned} $$</li>\n",
+        "\n",
+        "\n",
+        "যেখানে $x \\cdot y = x_0y_0 \\oplus x_1y_1 \\oplus \\ldots \\oplus x_{n-1}y_{n-1}$ হল বিটওয়াইজ পণ্যের সমষ্টি।\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>প্রথম নিবন্ধন পরিমাপ. লক্ষ্য করুন যে $\\vert 0 \\rangle ^{\\otimes n} = \\lvert \\frac{1}{2^n}\\sum_{x=0}^{2^n-1}(-1) পরিমাপের সম্ভাবনা ^{f(x)} \\rvert^2$, যা $f(x)$ ধ্রুবক হলে $1$ এবং $f(x)$ ভারসাম্য থাকলে $0$ মূল্যায়ন করে।</li>\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "\n",
+        "### 1.4 কেন এটি কাজ করে?<a id=\"why-does-this-work\"> </a>\n",
+        "\n",
+        "- **ধ্রুবক ওরাকল**\n",
+        "\n",
+        "ওরাকল যখন *ধ্রুবক থাকে* , তখন ইনপুট কিউবিটগুলিতে এটির কোন প্রভাব থাকে না (একটি বিশ্বব্যাপী পর্যায় পর্যন্ত), এবং ওরাকলকে জিজ্ঞাসা করার আগে এবং পরে কোয়ান্টাম অবস্থা একই থাকে। যেহেতু H-গেট তার নিজস্ব বিপরীত, ধাপ 4-এ আমরা প্রথম রেজিস্টারে $|00\\dots 0\\rangle$-এর প্রাথমিক কোয়ান্টাম অবস্থা পেতে ধাপ 2কে বিপরীত করি।\n",
+        "\n",
+        "# $$ H^{\\otimes n}\\begin{bmatrix} 1 \\ 0 \\ 0 \\ \\vdots \\ 0 \\end{bmatrix}\n",
+        "\n",
+        "# \\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix} \\quad \\xrightarrow{\\text{after } U_f} \\quad H^{\\otimes n}\\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix}\n",
+        "\n",
+        "\\begin{bmatrix} 1 \\ 0 \\ 0 \\ \\vdots \\ 0 \\end{bmatrix} $$\n",
+        "\n",
+        "- **সুষম ওরাকল**\n",
+        "\n",
+        "ধাপ 2 এর পরে, আমাদের ইনপুট রেজিস্টার গণনাগত ভিত্তিতে সমস্ত রাজ্যের সমান সুপারপজিশন। যখন ওরাকল *ভারসাম্যপূর্ণ* হয়, তখন ফেজ কিকব্যাক ঠিক অর্ধেক এই অবস্থাতে একটি নেতিবাচক পর্যায় যোগ করে:\n",
+        "\n",
+        "# $$ U_f \\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix}\n",
+        "\n",
+        "\\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} -1 \\ 1 \\ -1 \\ \\vdots \\ 1 \\end{bmatrix} $$\n",
+        "\n",
+        "ওরাকলকে জিজ্ঞাসা করার পরে কোয়ান্টাম অবস্থা ওরাকলকে জিজ্ঞাসা করার আগে কোয়ান্টাম অবস্থার অর্থোগোনাল। এইভাবে, ধাপ 4-এ, H-গেটগুলি প্রয়োগ করার সময়, আমাদের অবশ্যই একটি কোয়ান্টাম অবস্থার সাথে শেষ করতে হবে যা $|00\\dots 0\\rangle$ এর অর্থোগোনাল। এর মানে আমাদের কখনই অল-জিরো স্টেট পরিমাপ করা উচিত নয়।\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 2. উদাহরণ<a id=\"example\"></a>\n",
+        "\n",
+        "চলুন দুই বিট ব্যালেন্সড ফাংশনের জন্য একটি নির্দিষ্ট উদাহরণ দেওয়া যাক:\n",
+        "\n",
+        "একটি দুই-বিট ফাংশন বিবেচনা করুন $f(x_0,x_1)=x_0 \\oplus x_1$ যেমন\n",
+        "\n",
+        "$f(0,0)=0$\n",
+        "\n",
+        "$f(0,1)=1$\n",
+        "\n",
+        "$f(1,0)=1$\n",
+        "\n",
+        "$f(1,1)=0$\n",
+        "\n",
+        "এই দুই-বিট ওরালসের সংশ্লিষ্ট ফেজ ওরাকল হল $U_f \\lvert x_1, x_0 \\rangle = (-1)^{f(x_1, x_0)}\\lvert x \\rangle$\n",
+        "\n",
+        "$$\\lvert \\psi_0 \\rangle = \\lvert 0 0 \\rangle_{01} \\otimes \\lvert 1 \\rangle_{2} $$ উদাহরণ দিয়ে এই ওরাকলটি প্রত্যাশা অনুযায়ী কাজ করে কিনা তা আমরা এখন পরীক্ষা করব।\n",
+        "\n",
+        "<ol>\n",
+        "    <li>দুটি কিউবিটের প্রথম রেজিস্টার $|00\\rangle$ এবং দ্বিতীয় রেজিস্টার qubit $|1\\rangle$ এ শুরু করা হয়</li>\n",
+        "</ol>\n",
+        "\n",
+        "(উল্লেখ্য যে আমরা কিউবিট সূচী করতে সাবস্ক্রিপ্ট 0, 1, এবং 2 ব্যবহার করছি। \"01\" এর একটি সাবস্ক্রিপ্ট 0 এবং 1 কিউবিট ধারণকারী রেজিস্টারের অবস্থা নির্দেশ করে)\n",
+        "\n",
+        "$$\\lvert \\psi_0 \\rangle = \\lvert 0 0 \\rangle_{01} \\otimes \\lvert 1 \\rangle_{2} $$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>সমস্ত কিউবিটে হাদমার্ড প্রয়োগ করুন</li>\n",
+        "\n",
+        "\n",
+        "$$\\lvert \\psi_1 \\rangle = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle + \\lvert 0 1 \\rangle + \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)*{01} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)*{2}  $$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>ওরাকল ফাংশন $\\text{Q}_f = CX_{02}CX_{12}$, $$ \\begin{aligned} \\lvert \\psi_2 \\rangle = \\frac{1}{2\\sqrt{2 হিসাবে প্রয়োগ করা যেতে পারে }} \\left[ \\lvert 0 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 0 \\oplus 0 \\rangle - \\lvert 1 \\oplus 0 \\oplus 0 \\rangle \\right)_{2} \\ \\ + \\lvert 0 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 0 \\oplus 1 \\rangle - \\lvert 1 \\oplus 0 \\oplus 1 \\rangle \\right)_{2} \\\\ + \\ lvert 1 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 1 \\oplus 0 \\rangle - \\lvert 1 \\oplus 1 \\oplus 0 \\rangle \\right)_{2} \\\\ + \\lvert 1 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\oplus 1 \\oplus 1 \\rangle - \\lvert 1 \\oplus 1 \\oplus 1 \\rangle \\right)_{2} \\right] \\end{aligned} $$</li>\n",
+        "\n",
+        "\n",
+        "   <li>এটিকে সহজ করে, আমরা নিম্নলিখিতগুলি পাই: $$ \\begin{aligned} \\lvert \\psi_2 \\rangle &amp; = \\frac{1}{2\\sqrt{2}} \\left[ \\lvert 0 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} - \\lvert 0 1 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right) _{2} - \\lvert 1 0 \\rangle_{01} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} + \\lvert 1 1 \\rangle_{01} \\otimes \\ বাম( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} \\right] \\\\ &amp; = \\frac{1}{2} \\left( \\lvert 0 0 \\rangle - \\lvert 0 1 \\ rangle - \\lvert 1 0 \\rangle + \\lvert 1 1 \\rangle \\right)_{01} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} \\\\ &amp; = \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{0} \\otimes \\frac{1 }{\\sqrt{2}} \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{1} \\otimes \\frac{1}{\\sqrt{2}} \\left( \\lvert 0 \\ rangle - \\lvert 1 \\rangle \\right)_{2} \\end{aligned} $$</li>\n",
+        "\n",
+        "\n",
+        "   <li>প্রথম রেজিস্টারে হাদমার্ড প্রয়োগ করুন</li>\n",
+        "\n",
+        "\n",
+        "$$ \\lvert \\psi_3\\rangle = \\lvert 1 \\rangle_{0} \\otimes \\lvert 1 \\rangle_{1} \\otimes \\left( \\lvert 0 \\rangle - \\lvert 1 \\rangle \\right)_{2} $$\n",
+        "\n",
+        "   \n",
+        "\n",
+        "\n",
+        "   <li>প্রথম দুটি কিউবিট পরিমাপ করলে অ-শূন্য $11$ দেবে, একটি সুষম ফাংশন নির্দেশ করে।</li>\n",
+        "\n",
+        "\n",
+        "\n",
+        "আপনি নীচের উইজেট ব্যবহার করে অনুরূপ উদাহরণ চেষ্টা করতে পারেন. এইচ-গেট এবং ওরাকল যোগ করতে বোতাম টিপুন, সেলটি পুনরায় চালান এবং/অথবা বিভিন্ন ওরাকল চেষ্টা করার জন্য `case=\"constant\"` সেট করুন।"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+        "scrolled": true
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "from qiskit_textbook.widgets import dj_widget\n",
+        "dj_widget(size=\"small\", case=\"balanced\")"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 3. কোয়ান্টাম ওরাকল তৈরি করা<a id=\"creating-quantum-oracles\"> </a>\n",
+        "\n",
+        "আসুন কিছু ভিন্ন উপায় দেখি আমরা একটি কোয়ান্টাম ওরাকল তৈরি করতে পারি।\n",
+        "\n",
+        "একটি ধ্রুবক ফাংশনের জন্য, এটি সহজ:\n",
+        "\n",
+        "$\\qquad$ 1. যদি f(x) = 0 হয়, তাহলে রেজিস্টার 2-এর qubit-এ $I$ গেট প্রয়োগ করুন।<br> $\\qquad$ 2. যদি f(x) = 1 হয়, তাহলে রেজিস্টার 2-এর qubit-এ $X$ গেট প্রয়োগ করুন।\n",
+        "\n",
+        "একটি ভারসাম্যপূর্ণ ফাংশন জন্য, আমরা তৈরি করতে পারেন অনেক বিভিন্ন সার্কিট আছে. আমাদের সার্কিট ভারসাম্যের গ্যারান্টি দেওয়ার একটি উপায় হল রেজিস্টার 1-এ প্রতিটি কিউবিটের জন্য একটি সিএনওটি সম্পাদন করা, রেজিস্টার 2-এর কিউবিটকে লক্ষ্য হিসাবে। উদাহরণ স্বরূপ:\n",
+        "\n",
+        "![image2](images/deutsch_balanced1.svg)\n",
+        "\n",
+        "উপরের ছবিতে, উপরের তিনটি কিউবিট ইনপুট রেজিস্টার গঠন করে এবং নীচের কিউবিটটি আউটপুট রেজিস্টার। নিচের টেবিলে আমরা দেখতে পাচ্ছি কোন ইনপুট স্টেট কোন আউটপুট দেয়:\n",
+        "\n",
+        "ইনপুট বলে যে আউটপুট 0 | ইনপুট স্টেটস যে আউটপুট 1\n",
+        ":-: | :-:\n",
+        "000 | 001\n",
+        "011 | 100\n",
+        "101 | 010\n",
+        "110 | 111\n",
+        "\n",
+        "আমরা এক্স-গেটগুলিতে নির্বাচিত নিয়ন্ত্রণগুলি মোড়ানোর মাধ্যমে ভারসাম্য বজায় রেখে ফলাফলগুলি পরিবর্তন করতে পারি। উদাহরণস্বরূপ, সার্কিট এবং নীচের ফলাফল টেবিল দেখুন:\n",
+        "\n",
+        "![other_balanced_circuit](images/deutsch_balanced2.svg)\n",
+        "\n",
+        "ইনপুট বলে যে আউটপুট 0 | ইনপুট বলে যে আউটপুট 1\n",
+        ":-: | :-:\n",
+        "001 | 000\n",
+        "010 | 011\n",
+        "100 | 101\n",
+        "111 | 110"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 4. কিস্কিট বাস্তবায়ন<a id=\"implementation\"></a>\n",
+        "\n",
+        "আমরা এখন একটি থ্রি-বিট ফাংশনের উদাহরণের জন্য Deutsch-Jozsa অ্যালগরিদম বাস্তবায়ন করি, উভয় ধ্রুবক এবং ভারসাম্যপূর্ণ ওরাকল সহ। প্রথমে আমাদের আমদানি করা যাক:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 2,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ]
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "# initialization\n",
+        "import numpy as np\n",
+        "\n",
+        "# importing Qiskit\n",
+        "from qiskit import IBMQ, Aer\n",
+        "from qiskit.providers.ibmq import least_busy\n",
+        "from qiskit import QuantumCircuit, transpile\n",
+        "\n",
+        "# import basic plot tools\n",
+        "from qiskit.visualization import plot_histogram"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "এর পরে, আমরা আমাদের ওরাকলের জন্য ইনপুট রেজিস্টারের আকার সেট করি:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 3,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "# set the length of the n-bit input string. \n",
+        "n = 3"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 4.1 ধ্রুবক ওরাকল<a id=\"const_oracle\"></a>\n",
+        "\n",
+        "চলুন একটি ধ্রুবক ওরাকল তৈরি করে শুরু করা যাক, এই ক্ষেত্রে ইনপুট আউটপুটে কোন প্রভাব ফেলবে না তাই আমরা এলোমেলোভাবে আউটপুট qubit কে 0 বা 1 এ সেট করেছি:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 4,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ]
+      },
+      "outputs": [
+        {
+          "data": {
+            "image/svg+xml": [
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+            ],
+            "text/plain": [
+              "<Figure size 116.697x264.88 with 1 Axes>"
+            ]
+          },
+          "execution_count": 4,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# set the length of the n-bit input string. \n",
+        "n = 3\n",
+        "\n",
+        "const_oracle = QuantumCircuit(n+1)\n",
+        "\n",
+        "output = np.random.randint(2)\n",
+        "if output == 1:\n",
+        "    const_oracle.x(n)\n",
+        "\n",
+        "const_oracle.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 4.2 সুষম ওরাকল<a id=\"balanced_oracle\"></a>"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 5,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "balanced_oracle = QuantumCircuit(n+1)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "এর পরে, আমরা একটি সুষম ওরাকল তৈরি করি। যেমনটি আমরা বিভাগ 1b-এ দেখেছি, আমরা প্রতিটি ইনপুট কিউবিটকে নিয়ন্ত্রণ হিসাবে এবং আউটপুট বিটকে লক্ষ্য হিসাবে CNOTs সম্পাদন করে একটি ভারসাম্যপূর্ণ ওরাকল তৈরি করতে পারি। আমরা এক্স-গেটগুলিতে কিছু নিয়ন্ত্রণ মোড়ানোর মাধ্যমে 0 বা 1 দেওয়ার ইনপুট স্টেটগুলি পরিবর্তন করতে পারি। আসুন প্রথমে দৈর্ঘ্যের একটি `n` স্ট্রিং বেছে নেওয়া যাক যা নির্দেশ করে যে কোনটি মোড়ানো হবে:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 6,
+      "metadata": {
+        "scrolled": true
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "b_str = \"101\""
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "এখন আমাদের কাছে এই স্ট্রিংটি রয়েছে, আমরা এটিকে আমাদের এক্স-গেট স্থাপনের জন্য একটি কী হিসাবে ব্যবহার করতে পারি। আমাদের সার্কিটের প্রতিটি কিউবিটের জন্য, আমরা একটি X-গেট রাখি যদি `b_str` এ সংশ্লিষ্ট সংখ্যা `1` হয়, অথবা অঙ্কটি `0` হলে কিছুই করি না।"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 7,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 146.797x264.88 with 1 Axes>"
+            ]
+          },
+          "execution_count": 7,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "balanced_oracle = QuantumCircuit(n+1)\n",
+        "b_str = \"101\"\n",
+        "\n",
+        "# Place X-gates\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "balanced_oracle.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "এর পরে, আমরা প্রতিটি ইনপুট কিউবিটকে নিয়ন্ত্রণ হিসাবে এবং আউটপুট কিউবিটকে লক্ষ্য হিসাবে ব্যবহার করে আমাদের নিয়ন্ত্রিত-নট গেটগুলি করি:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 8,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 447.797x264.88 with 1 Axes>"
+            ]
+          },
+          "execution_count": 8,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "balanced_oracle = QuantumCircuit(n+1)\n",
+        "b_str = \"101\"\n",
+        "\n",
+        "# Place X-gates\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "\n",
+        "# Use barrier as divider\n",
+        "balanced_oracle.barrier()\n",
+        "\n",
+        "# Controlled-NOT gates\n",
+        "for qubit in range(n):\n",
+        "    balanced_oracle.cx(qubit, n)\n",
+        "\n",
+        "balanced_oracle.barrier()\n",
+        "balanced_oracle.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "অবশেষে, এক্স-গেটগুলিতে নিয়ন্ত্রণগুলি মোড়ানো শেষ করতে আমরা দুটি কক্ষ থেকে কোডটি পুনরাবৃত্তি করি:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 9,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ]
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 507.997x264.88 with 1 Axes>"
+            ]
+          },
+          "execution_count": 9,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "balanced_oracle = QuantumCircuit(n+1)\n",
+        "b_str = \"101\"\n",
+        "\n",
+        "# Place X-gates\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "\n",
+        "# Use barrier as divider\n",
+        "balanced_oracle.barrier()\n",
+        "\n",
+        "# Controlled-NOT gates\n",
+        "for qubit in range(n):\n",
+        "    balanced_oracle.cx(qubit, n)\n",
+        "\n",
+        "balanced_oracle.barrier()\n",
+        "\n",
+        "# Place X-gates\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "\n",
+        "# Show oracle\n",
+        "balanced_oracle.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "আমরা শুধু একটি সুষম ওরাকল তৈরি করেছি! ডয়েচ-জোজসা অ্যালগরিদম এটি সমাধান করতে পারে কিনা তা দেখতে বাকি আছে।\n",
+        "\n",
+        "### 4.3 সম্পূর্ণ অ্যালগরিদম<a id=\"full_alg\"></a>\n",
+        "\n",
+        "এখন সবকিছু একসাথে করা যাক. অ্যালগরিদমের এই প্রথম ধাপটি হল ইনপুট কিউবিট স্টেট $|{+}\\rangle$ এবং আউটপুট কিউবিট স্টেটে $|{-}\\rangle$:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 10,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 206.997x325.08 with 1 Axes>"
+            ]
+          },
+          "execution_count": 10,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "dj_circuit = QuantumCircuit(n+1, n)\n",
+        "\n",
+        "# Apply H-gates\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "\n",
+        "# Put qubit in state |->\n",
+        "dj_circuit.x(n)\n",
+        "dj_circuit.h(n)\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "এর পরে, এর ওরাকল প্রয়োগ করা যাক। এখানে আমরা উপরে তৈরি করা `balanced_oracle` প্রয়োগ করি:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 13,
+      "metadata": {
+        "scrolled": true
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 568.197x325.08 with 1 Axes>"
+            ]
+          },
+          "execution_count": 13,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "dj_circuit = QuantumCircuit(n+1, n)\n",
+        "\n",
+        "# Apply H-gates\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "\n",
+        "# Put qubit in state |->\n",
+        "dj_circuit.x(n)\n",
+        "dj_circuit.h(n)\n",
+        "\n",
+        "# Add oracle\n",
+        "dj_circuit = dj_circuit.compose(balanced_oracle)\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "অবশেষে, আমরা $n$-ইনপুট কিউবিটগুলিতে H-গেটগুলি সম্পাদন করি এবং আমাদের ইনপুট রেজিস্টার পরিমাপ করি:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 14,
+      "metadata": {
+        "scrolled": true
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 869.197x325.08 with 1 Axes>"
+            ]
+          },
+          "execution_count": 14,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "dj_circuit = QuantumCircuit(n+1, n)\n",
+        "\n",
+        "# Apply H-gates\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "\n",
+        "# Put qubit in state |->\n",
+        "dj_circuit.x(n)\n",
+        "dj_circuit.h(n)\n",
+        "\n",
+        "# Add oracle\n",
+        "dj_circuit = dj_circuit.compose(balanced_oracle)\n",
+        "\n",
+        "# Repeat H-gates\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "dj_circuit.barrier()\n",
+        "\n",
+        "# Measure\n",
+        "for i in range(n):\n",
+        "    dj_circuit.measure(i, i)\n",
+        "\n",
+        "# Display circuit\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "চলুন আউটপুট দেখিঃ"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 15,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 15,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# use local simulator\n",
+        "aer_sim = Aer.get_backend('aer_simulator')\n",
+        "results = aer_sim.run(dj_circuit).result()\n",
+        "answer = results.get_counts()\n",
+        "\n",
+        "plot_histogram(answer)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "আমরা উপরের ফলাফলগুলি থেকে দেখতে পাচ্ছি যে আমাদের `000` পরিমাপের 0% সম্ভাবনা রয়েছে। এটি সঠিকভাবে ভবিষ্যদ্বাণী করে যে ফাংশনটি ভারসাম্যপূর্ণ।\n",
+        "\n",
+        "### 4.4 সাধারণ সার্কিট<a id=\"general_circs\"></a>\n",
+        "\n",
+        "নীচে, আমরা একটি সাধারণ ফাংশন প্রদান করি যা ডয়েচ-জোজসা ওরাকল তৈরি করে এবং তাদের কোয়ান্টাম গেটে পরিণত করে। এটি `case` লাগে, (হয় `'balanced'` বা ' `constant` ', এবং `n` , ইনপুট রেজিস্টারের আকার:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 16,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ]
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "def dj_oracle(case, n):\n",
+        "    # We need to make a QuantumCircuit object to return\n",
+        "    # This circuit has n+1 qubits: the size of the input,\n",
+        "    # plus one output qubit\n",
+        "    oracle_qc = QuantumCircuit(n+1)\n",
+        "    \n",
+        "    # First, let's deal with the case in which oracle is balanced\n",
+        "    if case == \"balanced\":\n",
+        "        # First generate a random number that tells us which CNOTs to\n",
+        "        # wrap in X-gates:\n",
+        "        b = np.random.randint(1,2**n)\n",
+        "        # Next, format 'b' as a binary string of length 'n', padded with zeros:\n",
+        "        b_str = format(b, '0'+str(n)+'b')\n",
+        "        # Next, we place the first X-gates. Each digit in our binary string \n",
+        "        # corresponds to a qubit, if the digit is 0, we do nothing, if it's 1\n",
+        "        # we apply an X-gate to that qubit:\n",
+        "        for qubit in range(len(b_str)):\n",
+        "            if b_str[qubit] == '1':\n",
+        "                oracle_qc.x(qubit)\n",
+        "        # Do the controlled-NOT gates for each qubit, using the output qubit \n",
+        "        # as the target:\n",
+        "        for qubit in range(n):\n",
+        "            oracle_qc.cx(qubit, n)\n",
+        "        # Next, place the final X-gates\n",
+        "        for qubit in range(len(b_str)):\n",
+        "            if b_str[qubit] == '1':\n",
+        "                oracle_qc.x(qubit)\n",
+        "\n",
+        "    # Case in which oracle is constant\n",
+        "    if case == \"constant\":\n",
+        "        # First decide what the fixed output of the oracle will be\n",
+        "        # (either always 0 or always 1)\n",
+        "        output = np.random.randint(2)\n",
+        "        if output == 1:\n",
+        "            oracle_qc.x(n)\n",
+        "    \n",
+        "    oracle_gate = oracle_qc.to_gate()\n",
+        "    oracle_gate.name = \"Oracle\" # To show when we display the circuit\n",
+        "    return oracle_gate"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "আসুন একটি ফাংশন তৈরি করি যা এই ওরাকল গেটটি নেয় এবং এটিতে ডয়েচ-জোজসা অ্যালগরিদম সম্পাদন করে:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 17,
+      "metadata": {
+        "scrolled": true,
+        "tags": [
+          "thebelab-init"
+        ]
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "def dj_algorithm(oracle, n):\n",
+        "    dj_circuit = QuantumCircuit(n+1, n)\n",
+        "    # Set up the output qubit:\n",
+        "    dj_circuit.x(n)\n",
+        "    dj_circuit.h(n)\n",
+        "    # And set up the input register:\n",
+        "    for qubit in range(n):\n",
+        "        dj_circuit.h(qubit)\n",
+        "    # Let's append the oracle gate to our circuit:\n",
+        "    dj_circuit.append(oracle, range(n+1))\n",
+        "    # Finally, perform the H-gates again and measure:\n",
+        "    for qubit in range(n):\n",
+        "        dj_circuit.h(qubit)\n",
+        "    \n",
+        "    for i in range(n):\n",
+        "        dj_circuit.measure(i, i)\n",
+        "    \n",
+        "    return dj_circuit"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "অবশেষে, আসুন অ্যালগরিদমের সাথে খেলার জন্য এই ফাংশনগুলি ব্যবহার করি:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 18,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 628.397x385.28 with 1 Axes>"
+            ]
+          },
+          "execution_count": 18,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "n = 4\n",
+        "oracle_gate = dj_oracle('balanced', n)\n",
+        "dj_circuit = dj_algorithm(oracle_gate, n)\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "এবং এই সার্কিট চালানোর ফলাফল দেখুন:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 19,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 19,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "transpiled_dj_circuit = transpile(dj_circuit, aer_sim)\n",
+        "results = aer_sim.run(transpiled_dj_circuit).result()\n",
+        "answer = results.get_counts()\n",
+        "plot_histogram(answer)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 5. বাস্তব ডিভাইসের সাথে পরীক্ষা<a id=\"device\"></a>\n",
+        "\n",
+        "আমরা নিচের চিত্রের মতো বাস্তব ডিভাইসে সার্কিট চালাতে পারি। আমরা প্রথমে আমাদের সার্কিট পরিচালনা করতে পারে এমন কম-ব্যস্ত ডিভাইসটি সন্ধান করি।"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 20,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ]
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "least busy backend:  ibmq_belem\n"
+          ]
+        }
+      ],
+      "source": [
+        "# Load our saved IBMQ accounts and get the least busy backend device with greater than or equal to (n+1) qubits\n",
+        "IBMQ.load_account()\n",
+        "provider = IBMQ.get_provider(hub='ibm-q')\n",
+        "backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= (n+1) and\n",
+        "                                   not x.configuration().simulator and x.status().operational==True))\n",
+        "print(\"least busy backend: \", backend)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 21,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ]
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "Job Status: job has successfully run\n"
+          ]
+        }
+      ],
+      "source": [
+        "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n",
+        "from qiskit.tools.monitor import job_monitor\n",
+        "\n",
+        "transpiled_dj_circuit = transpile(dj_circuit, backend, optimization_level=3)\n",
+        "job = backend.run(transpiled_dj_circuit)\n",
+        "job_monitor(job, interval=2)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 22,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ]
+      },
+      "outputs": [
+        {
+          "data": {
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 22,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# Get the results of the computation\n",
+        "results = job.result()\n",
+        "answer = results.get_counts()\n",
+        "\n",
+        "plot_histogram(answer)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "আমরা দেখতে পাচ্ছি, সবচেয়ে সম্ভাব্য ফলাফল হল `1111` । অন্যান্য ফলাফলগুলি কোয়ান্টাম গণনার ত্রুটির কারণে। "
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 6. সমস্যা<a id=\"problems\"></a>\n",
+        "\n",
+        "1. আপনি একটি ভিন্ন ফর্ম একটি সুষম বা ধ্রুবক ওরাকল তৈরি করতে সক্ষম?\n",
+        "\n",
+        "2. ফাংশন `dj_problem_oracle` (নীচে) একটি গেট আকারে `n = 4` এর জন্য একটি Deutsch-Jozsa oracle প্রদান করে। গেটটি ইনপুট হিসাবে 5 কিউবিট নেয় যেখানে চূড়ান্ত qubit ( `q_4` ) হল আউটপুট qubit (উপরের ওরাকলের উদাহরণ হিসাবে)। আপনি `dj_problem_oracle` 1 এবং 5 এর মধ্যে বিভিন্ন পূর্ণসংখ্যা দিয়ে বিভিন্ন ওরাকল পেতে পারেন। প্রতিটি ওরাকল ভারসাম্যপূর্ণ বা ধ্রুবক কিনা তা নির্ধারণ করতে Deutsch-Jozsa অ্যালগরিদম ব্যবহার করুন ( **দ্রষ্টব্য:** এটি অত্যন্ত সুপারিশ করা হয় যে আপনি একটি বাস্তব ডিভাইসের পরিবর্তে `aer_simulator` ব্যবহার করে এই উদাহরণটি ব্যবহার করে দেখুন) ."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": null,
+      "metadata": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "from qiskit_textbook.problems import dj_problem_oracle\n",
+        "oracle = dj_problem_oracle(1)"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "## 7. References <a id=\"references\"></a>\n",
+        "\n",
+        "1. David Deutsch and Richard Jozsa (1992). \"Rapid solutions of problems by quantum computation\". Proceedings of the Royal Society of London A. 439: 553–558.  [doi:10.1098/rspa.1992.0167](https://doi.org/10.1098%2Frspa.1992.0167).\n",
+        "2. R. Cleve; A. Ekert; C. Macchiavello; M. Mosca (1998). \"Quantum algorithms revisited\". Proceedings of the Royal Society of London A. 454: 339–354. [doi:10.1098/rspa.1998.0164](https://doi.org/10.1098%2Frspa.1998.0164)."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 23,
+      "metadata": {
+      },
+      "outputs": [
+        {
+          "name": "stderr",
+          "output_type": "stream",
+          "text": [
+            "/usr/local/anaconda3/envs/terra-unstable/lib/python3.9/site-packages/qiskit/aqua/__init__.py:86: DeprecationWarning: The package qiskit.aqua is deprecated. It was moved/refactored to qiskit-terra For more information see <https://github.com/Qiskit/qiskit-aqua/blob/main/README.md#migration-guide>\n",
+            "  warn_package('aqua', 'qiskit-terra')\n"
+          ]
+        },
+        {
+          "data": {
+            "text/html": [
+              "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.19.0</td></tr><tr><td><code>qiskit-aer</code></td><td>0.9.1</td></tr><tr><td><code>qiskit-ignis</code></td><td>0.6.0</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.17.0</td></tr><tr><td><code>qiskit-aqua</code></td><td>0.9.5</td></tr><tr><td><code>qiskit</code></td><td>0.31.0</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.9.7</td></tr><tr><td>Python compiler</td><td>Clang 10.0.0 </td></tr><tr><td>Python build</td><td>default, Sep 16 2021 08:50:36</td></tr><tr><td>OS</td><td>Darwin</td></tr><tr><td>CPUs</td><td>8</td></tr><tr><td>Memory (Gb)</td><td>32.0</td></tr><tr><td colspan='2'>Fri Nov 05 14:18:55 2021 GMT</td></tr></table>"
+            ],
+            "text/plain": [
+              "<IPython.core.display.HTML object>"
+            ]
+          },
+          "metadata": {
+          },
+          "output_type": "display_data"
+        }
+      ],
+      "source": [
+        "import qiskit.tools.jupyter\n",
+        "%qiskit_version_table"
+      ]
+    }
+  ],
+  "metadata": {
+    "kernelspec": {
+      "display_name": "Python 3",
+      "language": "python",
+      "name": "python3"
+    },
+    "language_info": {
+      "codemirror_mode": {
+        "name": "ipython",
+        "version": 3
+      },
+      "file_extension": ".py",
+      "mimetype": "text/x-python",
+      "name": "python",
+      "nbconvert_exporter": "python",
+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 2
+}

From 37411282967ad9a098b28c657b35cdd12443cecf Mon Sep 17 00:00:00 2001
From: Frank Harkins <frankharkins@hotmail.co.uk>
Date: Fri, 17 Jun 2022 14:47:18 +0100
Subject: [PATCH 62/62] Add composer widget

---
 notebooks/basics/single-systems.ipynb | 11 ++++++++++-
 1 file changed, 10 insertions(+), 1 deletion(-)

diff --git a/notebooks/basics/single-systems.ipynb b/notebooks/basics/single-systems.ipynb
index 1cd048018..951923474 100644
--- a/notebooks/basics/single-systems.ipynb
+++ b/notebooks/basics/single-systems.ipynb
@@ -1518,7 +1518,16 @@
     "scrolled": true
    },
    "source": [
-    "(*** Interactive widget here.)"
+    "<!-- ::: q-block -->\n",
+    "\n",
+    "### Circuit sandbox\n",
+    "\n",
+    "    q-circuit-sandbox-widget(goal=\"circuit-sandbox\")\n",
+    "        .availableGates H X Z Y T S\n",
+    "        .instructions Drag the gates down onto the circuit to see how they transform the qubit.\n",
+    "        .explanation The 'matrix' display shows the unitary matrix of the circuit (i.e. all the gates' unitaries multiplied together). The 'state vector' display shows the state of the qubit after the gates act on it.\n",
+    "\n",
+    "<!-- ::: -->"
    ]
   },
   {