Randomized benchmarking under different gate sets

Kristine Boone, Arnaud Carignan-Dugas, Joel J. Wallman, and Joseph Emerson
Phys. Rev. A 99, 032329 – Published 20 March 2019

Abstract

We provide a comprehensive analysis of the differences between two important standards for randomized benchmarking (RB): the Clifford-group RB protocol proposed originally in Emerson et al. [J. Opt. B 7, S347 (2005)] and Dankert et al. [Phys. Rev. A 80, 012304 (2009)], and a variant of that RB protocol proposed by the NIST group in Knill et al. [Phys. Rev. A 77, 012307 (2008)]. While these two protocols are frequently conflated or presumed equivalent, we prove that they produce distinct exponential fidelity decays leading to differences of up to a factor of 3 in the estimated error rates under experimentally realistic conditions. These differences arise because the NIST RB protocol does not satisfy the unitary two-design condition for the twirl in the Clifford-group protocol and thus the decay rate depends on noninvariant features of the error model. Our analysis provides an important first step toward developing definitive standards for benchmarking quantum gates and a more rigorous theoretical underpinning for the NIST protocol and other RB protocols lacking a group-structure. We conclude by discussing the potential impact of these differences for estimating fault-tolerant overheads.

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  • Received 29 November 2018

DOI:https://doi.org/10.1103/PhysRevA.99.032329

©2019 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Kristine Boone1,2,3, Arnaud Carignan-Dugas1,2,4, Joel J. Wallman1,2,4, and Joseph Emerson1,2,4,5

  • 1Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • 2Quantum Benchmark Inc., 51 Breithaupt, Kitchener, Ontario N2H 5G5, Canada
  • 3Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • 4Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
  • 5Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada

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Issue

Vol. 99, Iss. 3 — March 2019

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