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Quantum Volume Estimation: Difference between revisions
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* The quantum volume treats the width and depth of a model circuit with equal importance and measures the largest square shaped (i.e., <math>m = d</math>) model circuit a quantum computer can implement successfully on average. | * The quantum volume treats the width and depth of a model circuit with equal importance and measures the largest square shaped (i.e., <math>m = d</math>) model circuit a quantum computer can implement successfully on average. | ||
* Given a model circuit <math>U</math>, a circuit-to-circuit transpiler finds an implementation <math>U'</math> for the target system such that <math>1- F_{avg}(U, U') \leq \epsilon \ll 1</math> | * Given a model circuit <math>U</math>, a circuit-to-circuit transpiler finds an implementation <math>U'</math> for the target system such that <math>1- F_{avg}(U, U') \leq \epsilon \ll 1</math> | ||
==Protocol Description== | |||
'''Function''': ComputeHeavyOutputs<math>(U, m)</math> | |||
'''Input''': <math>U, m</math> | |||
'''Output''': <math>H_U</math> | |||
* Obtain <math>p_U(x)</math> for <math>x \in \{0,1\}^m</math> | |||
* Sort in ascending order <math>p_0 \leq p_1 ... \leq p_{2^m -1}</math> | |||
* <math>p_{med} = (p_{2^{m-1}} + p_{2^{m-1}-1})/2 </math> | |||
* <math>H_U = \{x\in \{0,1\}^m</math> such that <math>p_U(x) > p_{med}\}</math> | |||
'''Function''': ComputeQuantumVolume | |||
'''Output''': Figure of merit: Quantum Volume, <math>V_Q</math> | |||
* For <math>i = 1, 2, ..., m</math>: | |||
** For <math>j = 1, 2, ..., d</math>: | |||
*** <math>d(m) = 0</math> | |||
*** <math>n_h = 0</math> | |||
*** For <math>k = 1, 2, ..., n_c</math>: | |||
**** Pick random model circuit <math>U</math> | |||
**** <math>H_U =</math> ComputeHeavyOutputs<math>(U, m)</math> | |||
**** Compile <math>U'</math> | |||
**** For <math>l = 1, 2, ..., n_s</math>: | |||
***** Get output <math>x</math> | |||
***** If <math>x\in H_U</math> then <math>n_h = n_h + 1</math> | |||
*** If <math>\frac{n_h-2\sqrt{n_h(n_s-n_h/n_c)}}{n_c n_S} > \frac{2}{3}</math> | |||
**** <math>d(m) = </math>max<math>(d(m), d)</math> | |||
**** Store data <math>(m, d(m))</math> | |||
* Calculate <math>V_Q</math> from stored data, where log<math>_2 V_Q</math> = argmax<math>_m</math> min<math>(m, d(m))</math> | |||
==Further Information== | |||
== Related Papers == | |||
* Andrew W. Cross et al (2011) arXiv:1811.12926v3: Validating quantum computers using randomized model circuits | |||
<div style='text-align: right;'>''*contributed by Rhea Parekh''</div> | |||