From cccc7ac35eff03fcb510c27e0f16b0492235368e Mon Sep 17 00:00:00 2001 From: Randy Tolentino Date: Tue, 9 Mar 2021 12:37:25 -0700 Subject: [PATCH] add small detail to formula (#6) --- .../quantum-hardware/measuring-quantum-volume.ipynb | 9 +++++++-- 1 file changed, 7 insertions(+), 2 deletions(-) diff --git a/textbook/notebooks/quantum-hardware/measuring-quantum-volume.ipynb b/textbook/notebooks/quantum-hardware/measuring-quantum-volume.ipynb index 83ff58b2c..9db924582 100644 --- a/textbook/notebooks/quantum-hardware/measuring-quantum-volume.ipynb +++ b/textbook/notebooks/quantum-hardware/measuring-quantum-volume.ipynb @@ -637,6 +637,11 @@ "meaning": "The number of times we run each circuit.", "say": "N S", "type": "Locally defined variable" + }, + "qv_z": { + "meaning": "Sets the threshold", + "say": "Z test", + "type": "Universally used notation" } } }, @@ -649,7 +654,7 @@ "\n", "Where nh is the number of heavy outputs measured, nc is the number of circuits we created, and ns is the number of times we run each circuit. But how do we decide what a “large enough” number of experiments is? Firstly, quantum volume requires at least 100 circuits are run, otherwise the test is invalid. Secondly, an adjusted threshold is used to ensure approximately 97% confidence:\n", "\n", - "$$\\frac{n_h-z\\sqrt{n_h(\\cssId{qv_ns}{n_s}-\\cssId{qv_nhnc}{\\frac{n_h}{n_c}})}}{n_cn_s}\\gt\\frac{2}{3}$$\n", + "$$\\frac{n_h -\\cssId{qv_z}{z}\\sqrt{n_h(\\cssId{qv_ns}{n_s}-\\cssId{qv_nhnc}{\\frac{n_h}{n_c}})}}{n_cn_s}\\gt\\frac{2}{3}$$\n", "\n", "Adding the new term (enclosed in the square root) requires a greater heavy output probability to satisfy the inequality, or a greater number of runs. Since the new term grows more slowly than the other terms, for a large number of runs this inequality resembles the simpler one shown above. If a quantum volume test satisfies the above inequality, there is at least a 97% chance the heavy output probability is greater than 2/3.\n", "\n", @@ -741,7 +746,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.0" + "version": "3.8.5" } }, "nbformat": 4,