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Title: What Randomized Benchmarking Actually Measures

Abstract

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 physicallymore » allowed (completely positive) representation of the imperfect gates.« less

Authors:
 [1];  [2];  [1];  [1];  [2]
  1. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
IARPA; USDOE
OSTI Identifier:
1406360
Report Number(s):
SAND-2017-10699J
Journal ID: ISSN 0031-9007; PRLTAO; 657513; TRN: US1703035
Grant/Contract Number:
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 119; Journal Issue: 13; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Proctor, Timothy, Rudinger, Kenneth, Young, Kevin, Sarovar, Mohan, and Blume-Kohout, Robin. What Randomized Benchmarking Actually Measures. United States: N. p., 2017. Web. doi:10.1103/physrevlett.119.130502.
Proctor, Timothy, Rudinger, Kenneth, Young, Kevin, Sarovar, Mohan, & Blume-Kohout, Robin. What Randomized Benchmarking Actually Measures. United States. doi:10.1103/physrevlett.119.130502.
Proctor, Timothy, Rudinger, Kenneth, Young, Kevin, Sarovar, Mohan, and Blume-Kohout, Robin. Thu . "What Randomized Benchmarking Actually Measures". United States. doi:10.1103/physrevlett.119.130502.
@article{osti_1406360,
title = {What Randomized Benchmarking Actually Measures},
author = {Proctor, Timothy and Rudinger, Kenneth and Young, Kevin and Sarovar, Mohan and Blume-Kohout, Robin},
abstractNote = {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.},
doi = {10.1103/physrevlett.119.130502},
journal = {Physical Review Letters},
number = 13,
volume = 119,
place = {United States},
year = {Thu Sep 28 00:00:00 EDT 2017},
month = {Thu Sep 28 00:00:00 EDT 2017}
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on September 28, 2018
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Cited by: 2works
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