Effect of noise correlations on randomized benchmarking

Ball, Harrison, Stace, Thomas M., Flammia, Steven T. and Biercuk, Michael J. (2016) Effect of noise correlations on randomized benchmarking. Physical Review A - Atomic, Molecular, and Optical Physics, 93 2: 022303.1-022303.23. doi:10.1103/PhysRevA.93.022303

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Author Ball, Harrison
Stace, Thomas M.
Flammia, Steven T.
Biercuk, Michael J.
Title Effect of noise correlations on randomized benchmarking
Journal name Physical Review A - Atomic, Molecular, and Optical Physics   Check publisher's open access policy
ISSN 1094-1622
2469-9926
Publication date 2016-02-01
Year available 2016
Sub-type Article (original research)
DOI 10.1103/PhysRevA.93.022303
Open Access Status File (Publisher version)
Volume 93
Issue 2
Start page 022303.1
End page 022303.23
Total pages 23
Place of publication College Park, MD, United States
Publisher American Physical Society
Collection year 2017
Language eng
Abstract Among the most popular and well-studied quantum characterization, verification, and validation techniques is randomized benchmarking (RB), an important statistical tool used to characterize the performance of physical logic operations useful in quantum information processing. In this work we provide a detailed mathematical treatment of the effect of temporal noise correlations on the outcomes of RB protocols. We provide a fully analytic framework capturing the accumulation of error in RB expressed in terms of a three-dimensional random walk in "Pauli space." Using this framework we derive the probability density function describing RB outcomes (averaged over noise) for both Markovian and correlated errors, which we show is generally described by a Γ distribution with shape and scale parameters depending on the correlation structure. Long temporal correlations impart large nonvanishing variance and skew in the distribution towards high-fidelity outcomes - consistent with existing experimental data - highlighting potential finite-sampling pitfalls and the divergence of the mean RB outcome from worst-case errors in the presence of noise correlations. We use the filter-transfer function formalism to reveal the underlying reason for these differences in terms of effective coherent averaging of correlated errors in certain random sequences. We conclude by commenting on the impact of these calculations on the utility of single-metric approaches to quantum characterization, verification, and validation.
Keyword Noise correlations
Randomized benchmarking
RB
Analytic framework
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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