What Randomized Benchmarking Actually Measures

Proctor, Timothy; Rudinger, Kenneth; Young, Kevin; Sarovar, Mohan; Blume-Kohout, Robin

doi:10.1103/physrevlett.119.130502

What Randomized Benchmarking Actually Measures

Journal Article · 28 September 2017 · Physical Review Letters

DOI:https://doi.org/10.1103/physrevlett.119.130502· OSTI ID:1406360

Proctor, Timothy ^[1]; Rudinger, Kenneth ^[2]; Young, Kevin ^[1]; Sarovar, Mohan ^[1]; Blume-Kohout, Robin ^[2]

Sandia National Lab. (SNL-CA), Livermore, CA (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Randomized benchmarking (RB) is widely used to measure an error rate of a set of quantum gates, by performing random circuits that would do nothing if the gates were perfect. In the limit of no finite-sampling error, the exponential decay rate of the observable survival probabilities, versus circuit length, yields a single error metric r. For Clifford gates with arbitrary small errors described by process matrices, r was believed to reliably correspond to the mean, over all Clifford gates, of the average gate infidelity between the imperfect gates and their ideal counterparts. We show that this quantity is not a well-defined property of a physical gate set. It depends on the representations used for the imperfect and ideal gates, and the variant typically computed in the literature can differ from r by orders of magnitude. We present new theories of the RB decay that are accurate for all small errors describable by process matrices, and show that the RB decay curve is a simple exponential for all such errors. Here, these theories allow explicit computation of the error rate that RB measures (r), but as far as we can tell it does not correspond to the infidelity of a physically allowed (completely positive) representation of the imperfect gates.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: IARPA; USDOE

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1406360

Report Number(s):: SAND-2017-10699J; PRLTAO; 657513; TRN: US1703035

Journal Information:: Physical Review Letters, Vol. 119, Issue 13; ISSN 0031-9007

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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