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>
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