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Cited by 20Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum many-body systems

Efficient unitarity randomized benchmarking of few-qubit Clifford gates

Open access
Dirkse, Bas, Helsen, Jonas, Wehner, Stephanie·2019·Physical Review A
DOI 10.1103/physreva.99.012315
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Abstract

Unitarity randomized benchmarking (URB) is an experimental procedure for estimating the coherence of implemented quantum gates independently of state preparation and measurement errors. These estimates of the coherence are measured by the unitarity. A central problem in this experiment is relating the number of data points to rigorous confidence intervals. In this work we provide a bound on the required number of data points for Clifford URB as a function of confidence and experimental parameters. This bound has favorable scaling in the regime of near-unitary noise and is asymptotically independent of the length of the gate sequences used. We also show that, in contrast to standard randomized benchmarking, a nontrivial number of data points is always required to overcome the randomness introduced by state preparation and measurement errors even in the limit of perfect gates. Our bound is sufficiently sharp to benchmark small-dimensional systems in realistic parameter regimes using a modest number of data points. For example, we show that the unitarity of single-qubit Clifford gates can be rigorously estimated using few hundred data points under the assumption of gate-independent noise. This is a reduction of orders of magnitude compared to previously known bounds.

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  • For theories in which γ(x) = <x,x>, the unitarity is invariant under changes of basis.

    “Similarly, for such theories, the unitarity is invariant under changes of basis [35,50].”

    From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [35]

    Section A, “Unitarity” (page not provided), states that the unitarity of a quantum channel is invariant under unitary transformations, supporting the basis-invariance point in that setting. It does not address the broader class of theories specified by γ(x) = ⟨x,x⟩, so that extension is not supported by this source. (LLM, conf=0.85)

    Experimental — accuracy not yet measured

  • Through randomized benchmarking, we can estimate the unitarity u(C) of the average error channel C induced by a computational gateset generating the Clifford group.

    “Through randomized benchmarking (RB) [35] we can estimate the unitarity u( C ) of the average error channel C induced by a computational gateset {U C } generating the Clifford group.”

    From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [35]

    The Introduction says unitarity randomized benchmarking estimates the unitarity of errors in a gate set, and Example 3 demonstrates an estimate for Clifford gates. But the Future work section says the analysis assumes gate-independent errors; it does not establish that the protocol estimates the unitarity of an average error channel for a general computational gateset that generates the Clifford group. Page numbers were not available in our copy. (LLM, conf=0.81)

    Experimental — accuracy not yet measured

  • The fidelity of a quantum channel is upper bounded by the unitarity.

    “The fidelity of a quantum channel is upper bounded by the unitarity [36]”

    From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [36]

  • The efficient unitarity RB protocol allows for rigorous bounds on the variance in the associated decay curve, and therefore on the value of unitarity extracted.

    “The protocol allows for rigorous bounds on the variance in the associated decay curve, and therefore the value of unitarity extracted.”

    From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [36]

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Authors
Dirkse, B., Helsen, J., & Wehner, S.
Affiliations
  • Centrum Wiskunde & Informatica (NL)
  • QuTech (NL)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2019-01-10
Volume
99
Issue
1
ISSN
  • 0556-2791 (ISSN-L)
  • 2469-9926
  • 2469-9934
DOI
10.1103/physreva.99.012315
OpenAlex
W2886708403
Cited by
20
References
41
Citations by year
2025: 1 · 2024: 2 · 2023: 2 · 2022: 2 · 2021: 8 · 2020: 2 · 2019: 3
FWCI
1.71
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (publishedVersion)
  • Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands (submittedVersion)
  • Data Archiving and Networked Services (DANS) (submittedVersion, other-oa)
  • Research Repository (Delft University of Technology) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Nederlandse Organisatie voor Wetenschappelijk Onderzoek
  • European Research Council
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
Keywords
Clifford gates, gate fidelity, sample size bounds, confidence intervals, state preparation and measurement errors, single-qubit gates

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