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Cited by 65Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum many-body systems

Efficient error characterization in quantum information processing

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Lévi, Benjamin, López, Cecilia C., Emerson, Joseph, Cory, D. G.·2007·Physical Review A
DOI 10.1103/physreva.75.022314
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Abstract

We describe how to use the fidelity decay as a tool to characterize the errors affecting a quantum information processor through a noise generator ${G}_{\ensuremath{\tau}}$. For weak noise, the initial decay rate of the fidelity proves to be a simple way to measure the magnitude of the different terms in ${G}_{\ensuremath{\tau}}$. When the generator has only terms associated with few-body couplings, our proposal is scalable. We present the explicit protocol for estimating the magnitude of the noise generators when the noise consists of only one- and two-body terms, and describe a method for measuring the parameters of more general noise models. The protocol focuses on obtaining the magnitude with which these terms affect the system during a time step of length $\ensuremath{\tau}$; measurement of this information has critical implications for assessing the scalability of fault-tolerant quantum computation in any physical setup.

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  • The protocol of [18] assumes noise independent of the chosen gate, in which case the fidelity decay curve averaged over randomly chosen unitaries is exponential in sequence length.

    “For instance [18] assumes the highly idealized situation of the noise being independent of the chosen gate, in which case the fidelity decay curve averaged over randomly chosen unitaries takes the form of an exponential (in the sequence length).”

    From Characterizing quantum gates via randomized benchmarking (2012) · cites this paper as [18]

  • The average fidelity of Λ is invariant under Clifford twirling.

    “Recall from Sec. (II B) that the average fidelity of Λ, denoted F ave , is invariant under Clifford twirling and so,”

    From Characterizing quantum gates via randomized benchmarking (2012) · cites this paper as [18]

  • Twirling a quantum operation over the Clifford group produces a depolarizing channel and the average fidelity is invariant under the twirling operation.

    “Thus twirling a quantum operation over the Clifford group produces a depolarizing channel and the average fidelity is invariant under the twirling operation.”

    From Characterizing quantum gates via randomized benchmarking (2012) · cites this paper as [18]

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Research works printed but not linked: 5

  1. [6]S. Bettelli, Phys. Rev. A , 69, 042310 (2004).
  2. [11]C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, W. K. Wootters, Phys. Rev. A 54 , 3824-3851 (1996); D. P. DiVincenzo, D. W. Leung, B. M. Terhal, IEEE Trans. In-
  3. [13]M. Po´ zniak, K. ˙ Zyczkowski, M. Ku´ s, J. Phys. A 31 , 10591071 (1998). Please see chao-dyn/9707006 for misprints corrections. · arXiv
  4. [20]W. Hoeffding, Journal of the American Statistical Association 58 , 301, 1330 (1963).
  5. [21]P. Mansfield and P. K. Grannell, Phys. Rev. B 12 , 3618 (1975), D. G. Cory, J. B. Miller, and A. N. Garroway, Journal of Magnetic Resonance, 90, 205-213 (1990).

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Authors
Lévi, B., López, C. C., Emerson, J., & Cory, D. G.
Affiliations
  • Massachusetts Institute of Technology (US)
  • University of Waterloo (CA)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2007-02-16
Volume
75
Issue
2
ISSN
  • 0556-2791 (ISSN-L)
  • 1050-2947
  • 1094-1622
DOI
10.1103/physreva.75.022314
OpenAlex
W2009654826
Cited by
65
References
32
Citations by year
2026: 1 · 2025: 4 · 2024: 1 · 2023: 5 · 2022: 3 · 2021: 8 · 2020: 6 · 2019: 1 · 2018: 9 · 2016: 1 · 2013: 2 · 2012: 5
FWCI
5.91
Type
journal article
Language
en
Open access
Licence
link.aps.org/licenses/aps-default-license (vor)
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
  • arXiv (Cornell University)
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
error characterization, fidelity decay, noise generator, weak noise, noise parameter estimation, noise models, fault-tolerant quantum computing, scalability, quantum information processing

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