Statistical analysis of randomized benchmarking

Harper, Robin; Hincks, Ian; Ferrie, Christopher; Flammia, Steven T.; Wallman, Joel J.

doi:10.1103/physreva.99.052350

Cited by 40 publications

(38 citation statements)

References 30 publications

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“…A similar method was explored in Ref. [12] to reduce the fitting parameters in order to derive multiplicative precision in standard RB. In addition to both of these advantages, we find that it also allows us to separate the analysis of the standard decay r from the effects of leakage errors and reduce the assumptions required in the derivation.…”

Section: Subspace Randomized Benchmarkingmentioning

confidence: 99%

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Subspace benchmarking high-fidelity entangling operations with trapped ions

Baldwin

Bjork

Gaebler

et al. 2020

Phys. Rev. Research

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We present a new and simplified two-qubit randomized benchmarking procedure that operates only in the symmetric subspace of a pair of qubits and is well suited for benchmarking trapped-ion systems. By performing benchmarking only in the symmetric subspace, we drastically reduce the experimental complexity, number of gates required, and run time. The protocol is demonstrated on trapped ions using collective single-qubit rotations and the Mølmer-Sørenson (MS) interaction to estimate an entangling gate error of 2(1) × 10 −3 . We analyze the expected errors in the MS gate and find that population remains mostly in the symmetric subspace. The errors that mix symmetric and anti-symmetric subspaces appear as leakage and we characterize them by combining our protocol with recently proposed leakage benchmarking. Generalizations and limitations of the protocol are also discussed. III. Subspace RB -Our constuction of SRB and howsubspace leakage is considered.IV. Extracting information from SRB -Analysis of how different errors are manifested in SRB.V. Experimental platform -A description of the SRB demonstration.VI. Results and discussion -Estimates of the subspace and leakage errors.VII. Generalized subspace RB -Extensions to other systems.arXiv:1911.00085v2 [quant-ph]

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Section: Subspace Randomized Benchmarkingmentioning

confidence: 99%

“…Subgroups of Pauli/Weyl gates, e.g. {1, X}, will also fix the asymptote [12] but will require additional assumptions for the leakage analysis. In RB, we estimate p( ) for different values of and fit the results to Eq.…”

Section: Appendix B: Standard Randomized Benchmarking Derivationmentioning

confidence: 99%

Subspace benchmarking high-fidelity entangling operations with trapped ions

Baldwin

Bjork

Gaebler

et al. 2020

Phys. Rev. Research

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“…We run mirror benchmarking on n = 6, 8, 10 qubits. For the largest circuits run in this experiment, with n = 10 and sequence length L = 16, corresponding to a two-qubit circuit depth of 32 and 160 total two-qubit gates, we obtain an average survival probability of 0.344 (18). The outline of this paper is as follows.…”

Section: Introductionmentioning

confidence: 99%

Theory of mirror benchmarking and demonstration on a quantum computer

Mayer¹,

Hall²,

Gatterman³

et al. 2021

Preprint

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A new class of protocols called mirror benchmarking was recently proposed to measure the systemlevel performance of quantum computers. These protocols involve circuits with random sequences of gates followed by mirroring, that is, inverting each gate in the sequence. We give a simple proof that mirror benchmarking leads to an exponential decay of the survival probability with sequence length, under the uniform noise assumption, provided the twirling group forms a 2-design. The decay rate is determined by a quantity that is a quadratic function of the error channel, and for certain types of errors is equal to the unitarity. This result yields a new method for estimating the coherence of noise. We present data from mirror benchmarking experiments run on the Honeywell System Model H1. This data constitutes a set of performance curves, indicating the success probability for random circuits as a function of qubit number and circuit depth.

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“…It was suggested that varying the number of sequences depending on Clifford length may improve the reliability of estimated decay rate [16]. Finding the best maximum Clifford length was also discussed in [17]. However, none of them addressed the problem of both optimizing Clifford lengths and the number of sequences at the same time.…”

Section: Introductionmentioning

confidence: 99%

Sampling Strategy Optimization for Randomized Benchmarking

Itoko¹,

Raymond²

2021

Preprint

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Randomized benchmarking (RB) is a widely used method for estimating the average fidelity of gates implemented on a quantum computing device. The stochastic error of the average gate fidelity estimated by RB depends on the sampling strategy (i.e., how to sample sequences to be run in the protocol). The sampling strategy is determined by a set of configurable parameters (an RB configuration) that includes Clifford lengths (a list of the number of independent Clifford gates in a sequence) and the number of sequences for each Clifford length. The RB configuration is often chosen heuristically and there has been little research on its best configuration. Therefore, we propose a method for fully optimizing an RB configuration so that the confidence interval of the estimated fidelity is minimized while not increasing the total execution time of sequences. By experiments on real devices, we demonstrate the efficacy of the optimization method against heuristic selection in reducing the variance of the estimated fidelity.

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Statistical analysis of randomized benchmarking

Cited by 40 publications

References 30 publications

Subspace benchmarking high-fidelity entangling operations with trapped ions

Subspace benchmarking high-fidelity entangling operations with trapped ions

Theory of mirror benchmarking and demonstration on a quantum computer

Sampling Strategy Optimization for Randomized Benchmarking

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