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Quantum Volume Estimation: Difference between revisions
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(Created page with "[https://journals.aps.org/pra/abstract/10.1103/PhysRevA.100.032328 Quantum Volume (QV)] is a single-number metric that can be measured using a concrete protocol on near-term q...") |
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* The data of achievable depth is gathered by sweeping over values of width <math>m</math> and depth <math>d</math> of the model circuit. | * The data of achievable depth is gathered by sweeping over values of width <math>m</math> and depth <math>d</math> of the model circuit. | ||
* Using all the data gathered, the quantum volume is computed. 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. | * Using all the data gathered, the quantum volume is computed. 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. | ||
==Notation== | |||
* <math>U</math>: Model circuit | |||
* <math>U'</math>: Implementation of the model circuit by the quantum transpiler | |||
* <math>m</math>: width of the model circuit | |||
* <math>d</math>: depth of the model circuit | |||
* <math>F_{avg}(U, U')</math>: Average fidelity between <math>U</math> and <math>U'</math> | |||
* <math>\epsilon</math>: approximation error | |||
* <math>d(m)</math>: Achievable depth, which is the largest <math>d</math> such that we are confident that the probability of observing a heavy output is greater than <math>2/3</math> | |||
* <math>V_Q</math>: Quantum Volume | |||
* <math>H_U</math>: Set of heavy outputs for a model circuit <math>U</math> | |||
* <math>x</math>: Outcome of executing <math>U'</math>, which is a observable bit string, <math>x \in \{0,1\}^m</math> | |||
* <math>p_U(x)</math>: Ideal output distribution for <math>U</math>. <math>p_U(x) = |\langle x|U|0\rangle|^2</math> | |||
* <math>p_{med}</math>: median of the set of probabilities | |||
* <math>n_c</math>: Number of repetitions, <math>n_c>100</math> | |||
* <math>n_s</math>: Number of repetitions | |||
==Hardware Requirements== | |||
* Quantum Computing device with a gate set | |||
* Measurement device | |||
==Properties== | |||
* '''Figure of merit''': Quantum Volume | |||
* Quantum computing systems with high-fidelity operations, high connectivity, large calibrated gate sets, and circuit rewriting tool chains are expected to have higher quantum volumes | |||
* The protocol can be implemented with any universal programmable quantum computing device | |||
* The method used to compute the heavy outputs from the ideal output distribution of the model circuit scales exponentially with the width <math>m</math>. | |||
* Ideally, the probability of observing a heavy output would be estimated using all of the qubits of a large device, but NISQ devices have appreciable error rates, so we begin with small model circuits and progress to larger ones. | |||
* 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> | |||