diff --git a/LOCALIZATION_CONTRIBUTORS b/LOCALIZATION_CONTRIBUTORS
index e1d6b85cf..0c998f1b1 100644
--- a/LOCALIZATION_CONTRIBUTORS
+++ b/LOCALIZATION_CONTRIBUTORS
@@ -43,16 +43,20 @@ Sungjoo Hwang | Denny-Hwang
 Dayeong Kang | tula3and
 Mingi Ryu | mingiryu
 Young Ju Tak | glucktak
+Sumin Jin | nineil91
 
 Indonesian (ID)
 
 Hanifan Rizki Nurahman | Hanifanrn
 Natasha Valentina | natashaval
 
-Portuguese (PT)
+Portuguese (PT_UN)
 
 Gustavo Mirapalheta | gustavomirapalheta
 Marco Antonio Barroca | MarcoBarroca
+André Galdino dos Santos | andregs2709
+Natália Capra Ferrazzo | nataliaferrazzo
+Omar Costa Hamido | omarcostahamido
 
 Simplified Chinese (ZH-CHS)
 
@@ -60,7 +64,7 @@ Yunzhe Zheng | Dran-Z
 Weixiao Sun | sunwx17
 Bin Liu | fjirsmliu
 Gang Ning | NG-Glen
-
+Mengyin Tan | Linxi
 
 Hindi (HI)
 
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/frontend/vue/components/MiniComposer/Circuit.vue b/frontend/vue/components/MiniComposer/Circuit.vue
index fdd73df6a..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
@@ -21,15 +22,16 @@
 
 <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 })
   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
new file mode 100644
index 000000000..749a02655
--- /dev/null
+++ b/frontend/vue/components/MiniComposer/CircuitSandboxWidget.vue
@@ -0,0 +1,283 @@
+<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>
+      <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"
+        :max-gates="MAX_GATES"
+      />
+    </div>
+    <div
+      ref="explanationRef"
+      class="mini-composer__explanation"
+    />
+    <div class="mini-composer__state-views">
+      <section>
+        <h1 class="mini-composer__state-views__title">
+          Matrix
+        </h1>
+        <SymbolicNotation
+          class="mini-composer__state-views__area"
+          :tex="matrixTex"
+        />
+      </section>
+      <section>
+        <h1 class="mini-composer__state-views__title">
+          State Vector
+        </h1>
+        <SymbolicNotation
+          class="mini-composer__state-views__area"
+          :tex="stateVectorTex"
+        />
+      </section>
+    </div>
+  </section>
+</template>
+
+<script lang="ts">
+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'
+import { ComposerGate, gateMatrix } from './composerTypes'
+import { GateName, IdentityState, StateMatrixToTexMatrix, StateMatrixToTexKetNotation } from './gateUtils'
+import SymbolicNotation from './SymbolicNotation.vue'
+
+class Props {
+  goal = prop<String>({ default: 'mini-composer-solved', required: true })
+}
+
+@Options({
+  components: {
+    Circuit,
+    GatesPool,
+    draggable,
+    SymbolicNotation,
+    SolutionStateIndicator,
+    PlayIcon
+  }
+})
+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) }
+  explanationRef = ref<HTMLDivElement | null>(null)
+  get explanation () { return (this.explanationRef as unknown as HTMLDivElement) }
+
+  MAX_GATES = 7
+
+  initialAvailableGates: ComposerGate[] = []
+  get availableGates (): ComposerGate[] {
+    return this.initialAvailableGates.map(gate => gate)
+  }
+
+  circuitState: ComposerGate[][] = [[]]
+
+  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())
+  }
+
+  get matrixTex () {
+    return StateMatrixToTexMatrix(this.matrixState)
+  }
+
+  get stateVectorTex () {
+    return StateMatrixToTexKetNotation(this.matrixState)
+  }
+
+  mounted () {
+    const instructionElement = this.configDiv.querySelector('.instructions')
+    const explanationElement = this.configDiv.querySelector('.explanation')
+    const availableGatesElement = this.configDiv.querySelector('.availableGates')
+
+    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 (availableGatesElement: HTMLElement) {
+    this.initialAvailableGates = []
+    if (availableGatesElement && availableGatesElement.textContent) {
+      this.initialAvailableGates = this.stringToGateNameArray(availableGatesElement.textContent)
+    }
+  }
+
+  stringToGateNameArray (text: string) : ComposerGate[] {
+    let lastGateId = 0
+    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: lastGateId++, rotation }
+        }
+        return { name: GateName.UNKNOWN, id: lastGateId++ }
+      })
+  }
+
+  onResetButton () {
+    this.circuitState = [[]]
+  }
+}
+</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;
+  grid-template-columns: 20rem 1fr;
+  grid-template-rows: min-content min-content 1fr min-content;
+  grid-template-areas:
+    "text text"
+    "gates lesson"
+    "circuit lesson"
+    "explanation lesson";
+
+  @include mq ($until: medium) {
+    grid-template-columns: 1fr;
+    grid-template-rows: repeat(5, min-content);
+    grid-template-areas:
+      "text"
+      "gates"
+      "circuit"
+      "explanation"
+      "lesson";
+  }
+
+  &__config-container {
+    display: none;
+  }
+
+  &__exercise-text {
+    @include type-style('body-long-01');
+    grid-area: text;
+    border-bottom: 1px solid $border-color;
+    padding: $spacing-05;
+  }
+  &__explanation {
+    @include type-style('body-long-01');
+    grid-area: explanation;
+    padding: $spacing-05;
+  }
+  &__gates {
+    grid-area: gates;
+    border-bottom: 1px solid $border-color;
+    padding: $spacing-05;
+    &__title {
+      margin: $spacing-03 0 $spacing-05 0;
+      @include type-style('heading-01');
+    }
+  }
+  &__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');
+    }
+    &__reset {
+      @include type-style('body-short-01');
+      grid-area: reset;
+      display: flex;
+      flex-flow: row;
+      gap: $spacing-03;
+      color: $link-color-tertiary;
+
+      &:hover {
+        color: $link-hover-color-tertiary;
+      }
+    }
+    &__circuit-lines {
+      grid-area: line;
+    }
+  }
+  &__state-views {
+    grid-area: lesson;
+    display: flex;
+    flex-direction: column;
+    gap: $spacing-05;
+    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;
+    }
+    &__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..e3f4ce594 100644
--- a/frontend/vue/components/MiniComposer/Gate.vue
+++ b/frontend/vue/components/MiniComposer/Gate.vue
@@ -9,6 +9,15 @@
     <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="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">
@@ -26,17 +35,7 @@ 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 +50,7 @@ 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
@@ -68,7 +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;
@@ -78,9 +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;
@@ -93,17 +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;
   }
@@ -113,5 +118,9 @@ export default class Gate extends Vue.with(Props) {
   &_keep {
     opacity: 0;
   }
+
+  :hover {
+    cursor: grab;
+  }
 }
 </style>
diff --git a/frontend/vue/components/MiniComposer/GatesPool.vue b/frontend/vue/components/MiniComposer/GatesPool.vue
index d0dc60d2e..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"
   >
@@ -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
@@ -36,7 +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/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..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 }">
@@ -27,13 +27,15 @@
 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 })
   circuitState = prop<ComposerGate[]>({ default: [], required: true })
   autoMeasureGate = prop<boolean>({ default: true, required: true })
+  maxGates = prop<Number>({ default: -1, required: true })
 }
 
 @Options({
@@ -50,6 +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>
 
diff --git a/frontend/vue/components/MiniComposer/SymbolicNotation.vue b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
new file mode 100644
index 000000000..f3be1424e
--- /dev/null
+++ b/frontend/vue/components/MiniComposer/SymbolicNotation.vue
@@ -0,0 +1,69 @@
+<template>
+  <div
+    ref="outputRef"
+    class="symbolic-notation"
+  />
+</template>
+
+<script lang="ts">
+import { ref } from '@vue/reactivity'
+import { Vue, prop } from 'vue-class-component'
+
+class Props {
+  tex = prop<String>({ default: '', required: true })
+}
+
+declare global {
+  interface Window {
+    MathJax: any
+  }
+}
+
+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.$watch('tex', () => this.renderTex())
+  }
+
+  renderTex () {
+    require('mathjax-full/es5/tex-chtml.js')
+
+    const MathJax = window.MathJax
+    const output = this.output
+
+    MathJax.startup.promise.then(() => {
+      MathJax.texReset()
+      const outputMetrics = MathJax.getMetricsFor(output)
+      const options = {
+        ...outputMetrics,
+        ...{ display: true }
+      }
+      MathJax
+        .tex2chtmlPromise(this.tex, options)
+        .then((node: HTMLElement) => {
+          output.childNodes.forEach((child) => {
+            child.remove()
+          })
+          output.appendChild(node)
+          MathJax.startup.document.clear()
+          MathJax.startup.document.updateDocument()
+          if (outputMetrics.containerWidth < node.clientWidth) {
+            node.style.fontSize = `${(outputMetrics.containerWidth / node.clientWidth) * 100 * 1.1}%`
+          }
+        }).catch((err: Error) => {
+          // If there was an error, put the message into the output instead
+          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..29c863854
--- /dev/null
+++ b/frontend/vue/components/MiniComposer/gateUtils.ts
@@ -0,0 +1,270 @@
+// eslint-disable-next-line import/named
+import { multiply, subtract, add, gcd, round } 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'
+}
+
+function neg (m: number[][]) {
+  return multiply(m, -1)
+}
+export interface StateMatrix {
+  A: number[][]
+  B: number[][]
+  C: number[][]
+  D: number[][]
+  m: number
+}
+
+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]],
+    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) {
+    return state
+  }
+}
+
+export const XGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K = [[0, 1], [1, 0]]
+    return {
+      A: multiply(K, state.A),
+      B: multiply(K, state.B),
+      C: multiply(K, state.C),
+      D: multiply(K, state.D),
+      m: state.m
+    }
+  }
+}
+
+export const YGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K = [[0, -1], [1, 0]]
+
+    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
+    }
+  }
+}
+
+export const ZGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K = [[1, 0], [0, -1]]
+
+    return {
+      A: multiply(K, state.A),
+      B: multiply(K, state.B),
+      C: multiply(K, state.C),
+      D: multiply(K, state.D),
+      m: state.m
+    }
+  }
+}
+
+export const HGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K = [[1, 1], [1, -1]]
+
+    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
+    }
+  }
+}
+
+export const SGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K1 = [[1, 0], [0, 0]]
+    const K2 = [[0, 0], [0, 1]]
+
+    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
+    }
+  }
+}
+
+export const TGate: QuantumGate = {
+  apply (state: StateMatrix) {
+    // Integer part
+    const K1 = [[2, 0], [0, 0]]
+    const K2 = [[0, 0], [0, 1]]
+
+    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 {
+      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
+    }
+  }
+}
+
+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 (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 = `${absNumerator}`
+  }
+
+  if (denominator !== 1 && m > 0) {
+    return `${sign}\\frac{${numeratorTex}}{${denominator}}`
+  } else {
+    return `${sign}${numeratorTex}`
+  }
+}
+
+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 = (a * a + b * b + c * c + d * d) === 0
+
+  if (isZero) {
+    return '0'
+  }
+
+  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)
+  }
+
+  return tex
+}
+
+export function StateMatrixToTexMatrix (state: StateMatrix) {
+  return `
+    \\begin{pmatrix}
+      ${StateMatrixElementToTex(state, { x: 0, y: 0 })} & ${StateMatrixElementToTex(state, { x: 0, y: 1 })}\\\\
+      ${StateMatrixElementToTex(state, { x: 1, y: 0 })} & ${StateMatrixElementToTex(state, { x: 1, y: 1 })}
+    \\end{pmatrix}
+  `
+}
+
+function parenthesis (text: string) {
+  return `\\left(${text}\\right)`
+}
+
+function valueKetTex (value: string, ket: 0 | 1) {
+  if (value === '0') {
+    return ''
+  }
+
+  const ketTex = `|${ket}\\rangle`
+  if (value === '1') {
+    return ketTex
+  }
+
+  const isMultiElement = value.includes('+') || value.lastIndexOf('-') > 1
+  const valueTex = isMultiElement ? parenthesis(value) : value
+
+  return `${valueTex}${ketTex}`
+}
+
+export function StateMatrixToTexKetNotation (state: StateMatrix) {
+  const zeroKetValue = StateMatrixElementToTex(state, { x: 0, y: 0 })
+  const oneKetValue = StateMatrixElementToTex(state, { x: 1, y: 0 })
+
+  const bothKets = zeroKetValue !== '0' && oneKetValue !== '0'
+
+  const zeroKetTex = valueKetTex(zeroKetValue, 0)
+  const oneKetTex = valueKetTex(oneKetValue, 1)
+
+  let joinTex = ''
+  if (bothKets && !oneKetTex.startsWith('-')) {
+    joinTex = '+'
+  }
+
+  return `
+    ${zeroKetTex}${joinTex}${oneKetTex}
+  `
+}
diff --git a/frontend/vue/components/UserAccount/ClassroomSection.vue b/frontend/vue/components/UserAccount/ClassroomSection.vue
index 58eff31dd..5319b812c 100644
--- a/frontend/vue/components/UserAccount/ClassroomSection.vue
+++ b/frontend/vue/components/UserAccount/ClassroomSection.vue
@@ -5,17 +5,26 @@
         {{ $translate("Classroom") }}
       </template>
       <template #description>
-        {{ $translate("This page shows your classroom activities in the Qiskit Textbook.") }}
+        {{
+          $translate(
+            "This page shows your classroom activities in the Qiskit Textbook."
+          )
+        }}
       </template>
     </UserAccountSectionHeader>
     <div class="classroom__create-syllabus">
       <AppCta
         class="classroom__create-syllabus__button"
-        :label="$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") }}
+        {{
+          $translate(
+            "Create a curated learning path for your students, using Qiskit Textbook Chapters, Labs, and Summer Schools"
+          )
+        }}
       </p>
     </div>
     <section class="classroom__content">
@@ -23,7 +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
@@ -38,38 +51,45 @@
 </template>
 
 <script lang="ts">
-import { defineComponent } from 'vue-demi'
-import AppCta from '../common/AppCta.vue'
-import UserAccountSectionHeader from './UserAccountSectionHeader.vue'
-import SyllabusCard from './SyllabusCard.vue'
-import { getSyllabi, Syllabus } from '../../../ts/syllabus'
+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",
+        segment: {
+          cta: "syllabus-create",
+          location: "user-account-classroom",
+        },
+      },
+    };
   },
   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();
@@ -86,7 +106,7 @@ export default defineComponent({
     }
 
     &__description {
-      @include type-style('body-long-01');
+      @include type-style("body-long-01");
     }
   }
 
@@ -94,12 +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;
     }
 
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/basics/single-systems.ipynb b/notebooks/basics/single-systems.ipynb
index e92a75772..7f76b80a1 100644
--- a/notebooks/basics/single-systems.ipynb
+++ b/notebooks/basics/single-systems.ipynb
@@ -1523,7 +1523,16 @@
     "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",
+    "<!-- ::: -->"
    ]
   },
   {
diff --git a/notebooks/examples/widgets.ipynb b/notebooks/examples/widgets.ipynb
index 1be2d125b..ef15d9750 100644
--- a/notebooks/examples/widgets.ipynb
+++ b/notebooks/examples/widgets.ipynb
@@ -7,6 +7,24 @@
     "# Widgets"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Circuit sandbox\n",
+    "\n",
+    "<!-- ::: 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 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"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {
@@ -53,13 +71,13 @@
    "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": [
diff --git a/package-lock.json b/package-lock.json
index 2052f13b9..2d2768de9 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -1,8 +1,28570 @@
 {
   "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",
+        "mathjax-full": "^3.2.2",
+        "mathjs": "^10.6.1",
+        "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"
+      },
+      "devDependencies": {
+        "@nuxtjs/eslint-config-typescript": "^10.0.0",
+        "@types/bcryptjs": "2.4.2",
+        "@types/express-flash": "0.0.2",
+        "@types/fs-extra": "^9.0.13",
+        "@types/jsdom": "^16.2.14",
+        "@types/lodash": "^4.14.180",
+        "@types/markdown-it": "^12.2.1",
+        "@types/node-fetch": "^2.6.1",
+        "@types/pug": "2.0.6",
+        "@types/validator": "13.6.6",
+        "@vue/cli-plugin-typescript": "4.5.13",
+        "@vue/cli-service": "4.5.13",
+        "@vue/compiler-sfc": "~3.1.5",
+        "axe-core": "^4.4.1",
+        "cross-env": "^7.0.3",
+        "cypress": "^9.5.0",
+        "cypress-axe": "^0.14.0",
+        "cypress-wait-until": "^1.7.2",
+        "eslint": "^8.11.0",
+        "fs-extra": "^10.0.0",
+        "js-yaml": "^4.1.0",
+        "jsdom": "^19.0.0",
+        "nano-staged": "^0.8.0",
+        "node-sass": "^6.0.0",
+        "nodemon": "^2.0.16",
+        "npm-run-all": "^4.1.5",
+        "rimraf": "^3.0.2",
+        "sass-loader": "^10.2.1",
+        "sass-mq": "^6.0.0",
+        "simple-git-hooks": "^2.7.0",
+        "start-server-and-test": "^1.14.0",
+        "tslib": "^2.3.1",
+        "vue-demi": "^0.12.1"
+      },
+      "engines": {
+        "node": ">=14 <17"
+      }
+    },
+    "node_modules/@achrinza/node-ipc": {
+      "version": "9.2.2",
+      "resolved": "https://registry.npmjs.org/@achrinza/node-ipc/-/node-ipc-9.2.2.tgz",
+      "integrity": "sha512-b90U39dx0cU6emsOvy5hxU4ApNXnE3+Tuo8XQZfiKTGelDwpMwBVgBP7QX6dGTcJgu/miyJuNJ/2naFBliNWEw==",
+      "dev": true,
+      "dependencies": {
+        "@node-ipc/js-queue": "2.0.3",
+        "event-pubsub": "4.3.0",
+        "js-message": "1.0.7"
+      },
+      "engines": {
+        "node": "8 || 10 || 12 || 14 || 16 || 17"
+      }
+    },
+    "node_modules/@babel/code-frame": {
+      "version": "7.16.7",
+      "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.16.7.tgz",
+      "integrity": "sha512-iAXqUn8IIeBTNd72xsFlgaXHkMBMt6y4HJp1tIaK465CWLT/fG1aqB7ykr95gHHmlBdGbFeWWfyB4NJJ0nmeIg==",
+      "dependencies": {
+        "@babel/highlight": "^7.16.7"
+      },
+      "engines": {
+        "node": ">=6.9.0"
+      }
+    },
+    "node_modules/@babel/generator": {
+      "version": "7.18.2",
+      "resolved": "https://registry.npmjs.org/@babel/generator/-/generator-7.18.2.tgz",
+      "integrity": "sha512-W1lG5vUwFvfMd8HVXqdfbuG7RuaSrTCCD8cl8fP8wOivdbtbIg2Db3IWUcgvfxKbbn6ZBGYRW/Zk1MIwK49mgw==",
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@@ -1281,18 +29855,18 @@
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@@ -1306,9 +29880,9 @@
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@@ -1320,17 +29894,17 @@
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@@ -1342,11 +29916,11 @@
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@@ -1354,22 +29928,22 @@
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+        "@jupyterlab/codemirror": "^3.4.3",
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@@ -1380,19 +29954,19 @@
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-        "@jupyterlab/translation": "^3.4.0",
-        "@jupyterlab/ui-components": "^3.4.0",
+      "version": "3.4.3",
+      "resolved": "https://registry.npmjs.org/@jupyterlab/filebrowser/-/filebrowser-3.4.3.tgz",
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+        "@jupyterlab/coreutils": "^5.4.3",
+        "@jupyterlab/docmanager": "^3.4.3",
+        "@jupyterlab/docregistry": "^3.4.3",
+        "@jupyterlab/services": "^6.4.3",
+        "@jupyterlab/statedb": "^3.4.3",
+        "@jupyterlab/statusbar": "^3.4.3",
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@@ -1407,16 +29981,16 @@
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-        "@jupyterlab/translation": "^3.4.0",
+      "version": "3.4.3",
+      "resolved": "https://registry.npmjs.org/@jupyterlab/logconsole/-/logconsole-3.4.3.tgz",
+      "integrity": "sha512-E5mif7dMk6//Aux/eOmdkONhya1h1SXAJ0IIyLof+qRXEjFSXisJfpN71lZqFIqIXSy0tpZJr1BK7KPxP/8t0A==",
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@@ -1425,14 +29999,14 @@
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@@ -1711,7 +30278,8 @@
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-          "integrity": "sha512-n/ShnvDi6FHbbVfviro+WojiFzv+s8MPMHBczVePfUpDJLwoLT0ht1l4YwBCbi8pJAveEEdnkHyPyTP/mzRfwg==",
-          "dev": true,
-          "requires": {
-            "safe-buffer": "~5.1.0"
-          }
-        },
         "strip-ansi": {
           "version": "3.0.1",
           "resolved": "https://registry.npmjs.org/strip-ansi/-/strip-ansi-3.0.1.tgz",
-          "integrity": "sha1-ajhfuIU9lS1f8F0Oiq+UJ43GPc8=",
+          "integrity": "sha512-VhumSSbBqDTP8p2ZLKj40UjBCV4+v8bUSEpUb4KjRgWk9pbqGF4REFj6KEagidb2f/M6AzC0EmFyDNGaw9OCzg==",
           "dev": true,
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@@ -21878,7 +50633,7 @@
         "to-regex-range": {
           "version": "2.1.1",
           "resolved": "https://registry.npmjs.org/to-regex-range/-/to-regex-range-2.1.1.tgz",
-          "integrity": "sha1-fIDBe53+vlmeJzZ+DU3VWQFB2zg=",
+          "integrity": "sha512-ZZWNfCjUokXXDGXFpZehJIkZqq91BcULFq/Pi7M5i4JnxXdhMKAK682z8bCW3o8Hj1wuuzoKcW3DfVzaP6VuNg==",
           "dev": true,
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@@ -22080,6 +50835,11 @@
       "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",
@@ -22194,9 +50954,10 @@
       }
     },
     "ws": {
-      "version": "7.5.7",
-      "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",
@@ -22227,6 +50988,11 @@
       "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",
@@ -22246,7 +51012,8 @@
     "xtend": {
       "version": "4.0.2",
       "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 +51142,9 @@
       }
     },
     "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 +51180,7 @@
         "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,
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@@ -22424,7 +51191,7 @@
         "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 +51206,7 @@
         "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 +51231,13 @@
         "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": {
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@@ -22479,13 +51246,13 @@
         "shebang-regex": {
           "version": "1.0.0",
           "resolved": "https://registry.npmjs.org/shebang-regex/-/shebang-regex-1.0.0.tgz",
-          "integrity": "sha1-2kL0l0DAtC2yypcoVxyxkMmO/qM=",
+          "integrity": "sha512-wpoSFAxys6b2a2wHZ1XpDSgD7N9iVjg29Ph9uV/uaP9Ex/KXlkTZTeddxDPSYQpgvzKLGJke2UU0AzoGCjNIvQ==",
           "dev": true
         },
         "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
         },
         "which": {
diff --git a/package.json b/package.json
index 8ffcfdefb..460d9dc9b 100644
--- a/package.json
+++ b/package.json
@@ -77,6 +77,8 @@
     "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",
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'] })
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')
 
diff --git a/translations/HowtoTranslate_QiskitTextbook_ja.pdf b/translations/HowtoTranslate_QiskitTextbook_ja.pdf
index 8b0d35b5e..8f738eb4d 100644
Binary files a/translations/HowtoTranslate_QiskitTextbook_ja.pdf and b/translations/HowtoTranslate_QiskitTextbook_ja.pdf differ
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": [
+              "<?xml version=\"1.0\" encoding=\"UTF-8\"?><!DOCTYPE svg  PUBLIC '-//W3C//DTD SVG 1.1//EN'  'http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd'><svg width=\"102.51pt\" height=\"214.38pt\" version=\"1.1\" viewBox=\"0 0 102.51 214.38\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><defs><style type=\"text/css\">*{stroke-linecap:butt;stroke-linejoin:round;}</style></defs><path d=\"m0 214.38h102.51v-214.38h-102.51z\" fill=\"#ffffff\"/><path d=\"m63.491 43.561h27.271\" clip-path=\"url(#p9c90efca23)\" fill=\"none\" stroke=\"#000000\" stroke-linecap=\"square\" stroke-width=\"2\"/><path d=\"m63.491 89.012h27.271\" clip-path=\"url(#p9c90efca23)\" fill=\"none\" stroke=\"#000000\" stroke-linecap=\"square\" stroke-width=\"2\"/><path d=\"m63.491 134.46h27.271\" clip-path=\"url(#p9c90efca23)\" fill=\"none\" stroke=\"#000000\" stroke-linecap=\"square\" stroke-width=\"2\"/><path d=\"m63.491 179.91h27.271\" clip-path=\"url(#p9c90efca23)\" fill=\"none\" stroke=\"#000000\" stroke-linecap=\"square\" stroke-width=\"2\"/><g clip-path=\"url(#p9c90efca23)\"><g transform=\"translate(36.363 48.012) scale(.1625 -.1625)\"><defs><path id=\"DejaVuSans-Oblique-71\" transform=\"scale(.015625)\" d=\"m2669 525q-231-303-546-460-314-156-695-156-531 0-833 358-301 358-301 986 0 506 186 978t533 847q225 244 517 375t614 131q387 0 637-153t363-462l100 525h578l-934-4813h-579l360 1844zm-1778 813q0-463 193-705 194-242 560-242 544 0 928 520t384 1264q0 450-199 689-198 239-569 239-272 0-504-127-231-126-403-370-181-256-286-600-104-343-104-668z\"/><path id=\"DejaVuSans-30\" transform=\"scale(.015625)\" d=\"m2034 4250q-487 0-733-480-245-479-245-1442 0-959 245-1439 246-480 733-480 491 0 736 480 246 480 246 1439 0 963-246 1442-245 480-736 480zm0 500q785 0 1199-621 414-620 414-1801 0-1178-414-1799-414-620-1199-620-784 0-1198 620-414 621-414 1799 0 1181 414 1801 414 621 1198 621z\"/></defs><use xlink:href=\"#DejaVuSans-Oblique-71\"/><use transform=\"translate(63.477 -16.406) scale(.7)\" xlink:href=\"#DejaVuSans-30\"/></g></g><g clip-path=\"url(#p9c90efca23)\"><g transform=\"translate(36.363 93.463) scale(.1625 -.1625)\"><defs><path id=\"DejaVuSans-31\" transform=\"scale(.015625)\" d=\"m794 531h1031v3560l-1122-225v575l1116 225h631v-4135h1031v-531h-2687v531z\"/></defs><use xlink:href=\"#DejaVuSans-Oblique-71\"/><use transform=\"translate(63.477 -16.406) scale(.7)\" xlink:href=\"#DejaVuSans-31\"/></g></g><g clip-path=\"url(#p9c90efca23)\"><g transform=\"translate(36.363 138.91) scale(.1625 -.1625)\"><defs><path id=\"DejaVuSans-32\" transform=\"scale(.015625)\" d=\"m1228 531h2203v-531h-2962v531q359 372 979 998 621 627 780 809 303 340 423 576 121 236 121 464 0 372-261 606-261 235-680 235-297 0-627-103-329-103-704-313v638q381 153 712 231 332 78 607 78 725 0 1156-363 431-362 431-968 0-288-108-546-107-257-392-607-78-91-497-524-418-433-1181-1211z\"/></defs><use xlink:href=\"#DejaVuSans-Oblique-71\"/><use transform=\"translate(63.477 -16.406) scale(.7)\" xlink:href=\"#DejaVuSans-32\"/></g></g><g clip-path=\"url(#p9c90efca23)\"><g transform=\"translate(36.363 184.36) scale(.1625 -.1625)\"><defs><path id=\"DejaVuSans-33\" transform=\"scale(.015625)\" d=\"m2597 2516q453-97 707-404 255-306 255-756 0-690-475-1069-475-378-1350-378-293 0-604 58t-642 174v609q262-153 574-231 313-78 654-78 593 0 904 234t311 681q0 413-289 645-289 233-804 233h-544v519h569q465 0 712 186t247 536q0 359-255 551-254 193-729 193-260 0-557-57-297-56-653-174v562q360 100 674 150t592 50q719 0 1137-327 419-326 419-882 0-388-222-655t-631-370z\"/></defs><use xlink:href=\"#DejaVuSans-Oblique-71\"/><use transform=\"translate(63.477 -16.406) scale(.7)\" xlink:href=\"#DejaVuSans-33\"/></g></g><defs><clipPath id=\"p9c90efca23\"><rect x=\"7.2\" y=\"7.2\" width=\"88.107\" height=\"199.98\"/></clipPath></defs></svg>"
+            ],
+            "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": {
+            "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": [
+        "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": [
+        {
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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
+}
diff --git a/translations/es/ch-algorithms/deutsch-jozsa.ipynb b/translations/es/ch-algorithms/deutsch-jozsa.ipynb
new file mode 100644
index 000000000..8cd553e42
--- /dev/null
+++ b/translations/es/ch-algorithms/deutsch-jozsa.ipynb
@@ -0,0 +1,1103 @@
+{
+  "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": {
+      },
+      "source": [
+        "## 1. Introducción <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 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",
+        "$$ f({x_0,x_1,x_2,...}) \\rightarrow 0 \\textrm{ o } 1 \\textrm{ , donde } x_n \\textrm{ es } 0 \\textrm{ o } 1$$\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 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",
+        "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",
+        "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 $2^{n-1}+1$."
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 1.3 Solución Cuántica <a id=\"quantum-solution\"> </a>\n",
+        "\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",
+        "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>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",
+        "\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>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",
+        "\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 ¿Por qué funciona esto? <a id=\"why-does-this-work\"> </a>\n",
+        "\n",
+        "- **    Oráculo Constante**\n",
+        "\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",
+        "# $$ H^{\\otimes n}\\begin{bmatrix} 1 \\ 0 \\ 0 \\ \\vdots \\ 0 \\end{bmatrix}\n",
+        "\n",
+        "# \\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix} \\quad \\xrightarrow{\\text{after } U_f} \\quad H^{\\otimes n}\\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix}\n",
+        "\n",
+        "\\begin{bmatrix} 1 \\ 0 \\ 0 \\ \\vdots \\ 0 \\end{bmatrix} $$\n",
+        "\n",
+        "- **Oráculo Balanceado**\n",
+        "\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",
+        "# $$ U_f \\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} 1 \\ 1 \\ 1 \\ \\vdots \\ 1 \\end{bmatrix}\n",
+        "\n",
+        "\\tfrac{1}{\\sqrt{2^n}}\\begin{bmatrix} -1 \\ 1 \\ -1 \\ \\vdots \\ 1 \\end{bmatrix} $$\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. Ejemplo Resuelto <a id=\"example\"></a>\n",
+        "\n",
+        "Veamos un ejemplo específico para una función balanceada de dos bits:\n",
+        "\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",
+        "$f(0,1)=1$\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>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>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",
+        "\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. 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. 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",
+        "![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. 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:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 2,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ]
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "# inicialización\n",
+        "import numpy as np\n",
+        "\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",
+        "# importar herramientas básicas de graficación\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": {
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "# establece la longitud de la cadena de entrada de n bits.\n",
+        "n = 3"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "### 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:"
+      ]
+    },
+    {
+      "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": [
+        "# establece la longitud de la cadena de entrada de n bits.\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 Oráculo Balanceado <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": {
+      },
+      "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",
+        "# Colocar compuertas X\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": {
+      },
+      "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",
+        "# Colocar compuertas X\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "\n",
+        "# Usar una barrera como divisor\n",
+        "balanced_oracle.barrier()\n",
+        "\n",
+        "# Compuertas NOT controladas\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"
+        ]
+      },
+      "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",
+        "# Colocar compuertas X\n",
+        "for qubit in range(len(b_str)):\n",
+        "    if b_str[qubit] == '1':\n",
+        "        balanced_oracle.x(qubit)\n",
+        "\n",
+        "# Usar una barrera como divisor\n",
+        "balanced_oracle.barrier()\n",
+        "\n",
+        "# Compuertas NOT controladas\n",
+        "for qubit in range(n):\n",
+        "    balanced_oracle.cx(qubit, n)\n",
+        "\n",
+        "balanced_oracle.barrier()\n",
+        "\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",
+        "# Mostrar el oráculo\n",
+        "balanced_oracle.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "¡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 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 $|{-}\\rangle$:"
+      ]
+    },
+    {
+      "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",
+        "# Aplicar compuertas H\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "\n",
+        "# Poner el qubit en el estado |->\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
+      },
+      "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",
+        "# Aplicar compuertas H\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "\n",
+        "# Poner el qubit en el estado |->\n",
+        "dj_circuit.x(n)\n",
+        "dj_circuit.h(n)\n",
+        "\n",
+        "# Agregar el oráculo\n",
+        "dj_circuit = dj_circuit.compose(balanced_oracle)\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "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
+      },
+      "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",
+        "# Aplicar compuertas H\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "\n",
+        "# Poner el qubit en el estado |->\n",
+        "dj_circuit.x(n)\n",
+        "dj_circuit.h(n)\n",
+        "\n",
+        "# Agregar el oráculo\n",
+        "dj_circuit = dj_circuit.compose(balanced_oracle)\n",
+        "\n",
+        "# Repetir compuertas H\n",
+        "for qubit in range(n):\n",
+        "    dj_circuit.h(qubit)\n",
+        "dj_circuit.barrier()\n",
+        "\n",
+        "# Medir\n",
+        "for i in range(n):\n",
+        "    dj_circuit.measure(i, i)\n",
+        "\n",
+        "# Mostrar el circuito\n",
+        "dj_circuit.draw()"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "Veamos la salida:"
+      ]
+    },
+    {
+      "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": [
+        "# 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",
+        "\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 Circuitos Generalizados <a id=\"general_circs\"></a>\n",
+        "\n",
+        "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:"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 16,
+      "metadata": {
+        "tags": [
+          "thebelab-init"
+        ]
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "def dj_oracle(case, n):\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",
+        "    # Primero, tratemos el caso en el que oráculo está balanceado\n",
+        "    if case == \"balanced\":\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",
+        "        # A continuación, formatea 'b' como una cadena binaria de longitud 'n', rellenada con ceros:\n",
+        "        b_str = format(b, '0'+str(n)+'b')\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",
+        "        # 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",
+        "        # 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",
+        "    # Caso en el que oráculo es constante\n",
+        "    if case == \"constant\":\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\" # Para mostrar cuando presentamos el circuito\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"
+        ]
+      },
+      "outputs": [
+
+      ],
+      "source": [
+        "def dj_algorithm(oracle, n):\n",
+        "    dj_circuit = QuantumCircuit(n+1, n)\n",
+        "    # Configurar el qubit de salida:\n",
+        "    dj_circuit.x(n)\n",
+        "    dj_circuit.h(n)\n",
+        "    # Y configurar el registro de entrada:\n",
+        "    for qubit in range(n):\n",
+        "        dj_circuit.h(qubit)\n",
+        "    # Agreguemos la compuerta del oráculo a nuestro circuito:\n",
+        "    dj_circuit.append(oracle, range(n+1))\n",
+        "    # Finalmente, ejecutar las compuertas H nuevamente y medir:\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": {
+      },
+      "source": [
+        "Y observa los resultados de ejecutar este circuito:"
+      ]
+    },
+    {
+      "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. 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."
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 20,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ]
+      },
+      "outputs": [
+        {
+          "name": "stdout",
+          "output_type": "stream",
+          "text": [
+            "backend menos ocupado:  ibmq_belem\n"
+          ]
+        }
+      ],
+      "source": [
+        "# 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(\"backend menos ocupado: \", 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": [
+        "# 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)"
+      ]
+    },
+    {
+      "cell_type": "code",
+      "execution_count": 22,
+      "metadata": {
+        "tags": [
+          "uses-hardware"
+        ]
+      },
+      "outputs": [
+        {
+          "data": {
+            "image/svg+xml": [
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+            ],
+            "text/plain": [
+              "<Figure size 504x360 with 1 Axes>"
+            ]
+          },
+          "execution_count": 22,
+          "metadata": {
+          },
+          "output_type": "execute_result"
+        }
+      ],
+      "source": [
+        "# Obtener los resultados del cálculo\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": {
+      },
+      "source": [
+        "## 6. Problemas <a id=\"problems\"></a>\n",
+        "\n",
+        "1. ¿Eres capaz de crear un oráculo balanceado o constante de una forma diferente?\n",
+        "\n",
+        "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)."
+      ]
+    },
+    {
+      "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. 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)."
+      ]
+    },
+    {
+      "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
+}
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..e833f7c6c
--- /dev/null
+++ b/translations/es/ch-machine-learning/machine-learning-qiskit-pytorch.ipynb
@@ -0,0 +1,742 @@
+{
+  "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",
+        "## Contenido\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",
+        "###### 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",
+        "###### 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",
+        "<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)**. "
+      ]
+    },
+    {
+      "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. ¡Programemos! <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": {
+      },
+      "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": {
+      },
+      "source": [
+        "Probemos la implementación"
+      ]
+    },
+    {
+      "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",
+        "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."
+      ]
+    },
+    {
+      "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": {
+      },
+      "source": [
+        "#### Datos de entrenamiento"
+      ]
+    },
+    {
+      "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": {
+      },
+      "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": {
+      },
+      "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 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)."
+      ]
+    },
+    {
+      "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
+}
diff --git a/translations/ja/ch-algorithms/bernstein-vazirani.ipynb b/translations/ja/ch-algorithms/bernstein-vazirani.ipynb
index fefc0c2d6..bce1f136f 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": [
+  "cells": [
     {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "7527f4488c994a27b571c49bbdbe7181",
-       "version_major": 2,
-       "version_minor": 0
+      "cell_type": "markdown",
+      "metadata": {
+        "tags": [
+          "remove_cell"
+        ]
       },
-      "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"
       ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
     },
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-       "version_major": 2,
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+      "cell_type": "markdown",
+      "metadata": {
       },
-      "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。"
       ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
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-       "model_id": "5033beeb5ed64cd3b0a8643b779b114d",
-       "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\\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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+      "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",
+        "<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",
+        "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",
+        "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",
+        "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",
+        "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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+        "%qiskit_version_table"
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+      "pygments_lexer": "ipython3",
+      "version": "3.9"
+    }
+  },
+  "nbformat": 4,
+  "nbformat_minor": 2
 }
diff --git a/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb b/translations/ja/ch-algorithms/defining-quantum-circuits.ipynb
index 9cacb7ca0..6fcae2750 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",
+        "![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",
+        "### 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",
+        "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"
+      ]
+    }
+  ],
+  "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
 }
diff --git a/translations/ja/intro/describing-quantum-computers.ipynb b/translations/ja/intro/describing-quantum-computers.ipynb
new file mode 100644
index 000000000..a8edcf732
--- /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",
+        "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",
+        "$$\\class{x-ket}{|x\\rangle} \\class{def-equal}{:=} \\begin{bmatrix}\\cssId{_amp-0-0}{\\sqrt{\\tfrac{1}{2}}} \\ \\cssId{_amp-1-0}{\\sqrt{\\tfrac{1}{2}}} \\ \\cssId{_amp-2-0}{0} \\ \\cssId{_amp-3-0}{0} \\end{bmatrix}$$\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",
+        "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",
+        "<!-- ::: .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",
+        "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",
+        "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",
+        "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",
+        "<!-- ::: q-block.exercise -->\n",
+        "\n",
+        "### クイッククイズ\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"quiz2\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\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",
+        "<!-- ::: .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",
+        "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",
+        "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",
+        "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",
+        "### クイッククイズ\n",
+        "\n",
+        "<!-- ::: q-quiz(goal=\"intro-describing-3\") -->\n",
+        "\n",
+        "<!-- ::: .question -->\n",
+        "\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",
+        "<!-- ::: .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",
+        "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",
+        "<!-- ::: .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",
+        "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",
+        "（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",
+        "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。"
+      ]
+    }
+  ],
+  "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
+}
diff --git a/translations/ja/quantum-machine-learning/encoding.ipynb b/translations/ja/quantum-machine-learning/encoding.ipynb
new file mode 100644
index 000000000..a68cc0be1
--- /dev/null
+++ b/translations/ja/quantum-machine-learning/encoding.ipynb
@@ -0,0 +1,592 @@
+{
+  "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": {
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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",
+        "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",
+        "<!-- ::: 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",
+        "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:"
+      ]
+    },
+    {
+      "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",
+        "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",
+        "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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+      ],
+      "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",
+        "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。"
+      ]
+    },
+    {
+      "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": {
+      },
+      "source": [
+        "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:"
+      ]
+    },
+    {
+      "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",
+        "### クイッククイズ\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": [
+        "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>"
+      ]
+    },
+    {
+      "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
+}
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
diff --git a/translations/ko/ch-algorithms/bernstein-vazirani.ipynb b/translations/ko/ch-algorithms/bernstein-vazirani.ipynb
new file mode 100644
index 000000000..76ad38edc
--- /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",
+        "입력(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",
+        "$$ H^{\\otimes 2}|a\\rangle = \\frac{1}{2}\\sum_{x\\in {0,1}^2} (-1)^{a\\cdot x}|x\\ 범위 $$\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": {
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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
+}
diff --git a/translations/ko/ch-states/introduction.ipynb b/translations/ko/ch-states/introduction.ipynb
new file mode 100644
index 000000000..aaaab4a1a
--- /dev/null
+++ b/translations/ko/ch-states/introduction.ipynb
@@ -0,0 +1,107 @@
+{
+  "cells": [
+    {
+      "cell_type": "markdown",
+      "metadata": {
+        "tags": [
+          "remove_cell"
+        ]
+      },
+      "source": [
+        "# 소개\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "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."
+      ]
+    },
+    {
+      "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",
+        "### 간단한 연습\n",
+        "\n",
+        "다음 중 *비트* 에 대한 설명으로 옳은 것은?\n",
+        "\n",
+        "- 정보의 가장 작은 단위: `0` 또는 `1`\n",
+        "- 목수가 사용하는 대패의 날\n",
+        "- 말의 입에 물리는 재갈"
+      ]
+    },
+    {
+      "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"
+          }
+        }
+      },
+      "source": [
+        "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",
+        "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"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "![이미지2](images/bloch.png)\n"
+      ]
+    },
+    {
+      "cell_type": "markdown",
+      "metadata": {
+      },
+      "source": [
+        "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",
+        "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."
+      ]
+    }
+  ],
+  "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
+}
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
+}