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Cited by 535Quantum Computing Algorithms and ArchitectureQuantum Information and CryptographyQuantum many-body systems

Noise tailoring for scalable quantum computation via randomized compiling

Open access
Wallman, Joel J., Emerson, Joseph·2016·Physical Review A
DOI 10.1103/physreva.94.052325
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Abstract

Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors are even partially coherent, they present a major obstacle to performing robust computations. Here, we propose a method for introducing independent random single-qubit gates into the logical circuit in such a way that the effective logical circuit remains unchanged. We prove that this randomization tailors the noise into stochastic Pauli errors, which can dramatically reduce error rates while introducing little or no experimental overhead. Moreover, we prove that our technique is robust to the inevitable variation in errors over the randomizing gates and numerically illustrate the dramatic reductions in worst-case error that are achievable. Given such tailored noise, gates with significantly lower fidelity---comparable to fidelities realized in current experiments---are sufficient to achieve fault-tolerant quantum computation. Furthermore, the worst-case error rate of the tailored noise can be directly and efficiently measured through randomized benchmarking protocols, enabling a rigorous certification of the performance of a quantum computer.

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Crossref · 10.1103/physreva.94.052325

Cites

8 of 8 references verified0 citation errors · 0 not checkable

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  • Further near-term experiments exploring quantum error correction are bound to advance our understanding of noise in quantum devices, and to suggest more effective techniques for noise mitigation and device validation.

    “Further near-term experiments exploring quantum error correction are bound to advance our understanding of noise in quantum devices, and to suggest more effective techniques for noise mitigation [53, 54] and device validation [55].”

    From Quantum Computing in the NISQ era and beyond (2018) · cites this paper as [54]

  • For hiding, one must consider the set of isometric channels to capture quantum theory's no-hiding theorem, as well as the set of reversible channels for perfect hiding.

    “For hiding, we must consider the set of isometric channels to capture quantum theory's no-hiding theorem-as well as the set of reversible channels for perfect hiding [51].”

    From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [51]

    The passage on channels in section C (p. 4) concerns tailoring gate noise into Pauli noise, not hiding information. Searches for the no-hiding theorem, isometric channels, and reversible channels found no passage in our copy addressing the claimed distinction. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

  • For quantum theory, a channel E is reversible if and only if E(ρ), E(τ) = c ρ, τ for all states ρ, τ and some constant c > 0.

    “For quantum theory, a channel E is reversible if and only if E (ρ), E (τ ) = c ρ, τ(A5) for all states ρ, τ and some constant c > 0 [51].”

    From Simple formulation of no-cloning and no-hiding that admits efficient and robust verification (2024) · cites this paper as [51]

    The discussion of channels in “Randomized compiling” (p. 3) concerns stochastic noise, while “Methods” (pp. 7–8) concerns bounds on noisy circuits. Neither states a criterion for channel reversibility based on inner products of all pairs of states. Searches for reversibility and inner-product preservation found no passage addressing the claimed equivalence. (LLM, conf=0.75)

    Experimental — accuracy not yet measured

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Cites

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Research works printed but not linked: 6

  1. [20]E. Knill, D. Leibfried, R. Reichle, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, Phys. Rev. A 77, 012307 (2008).
  2. [23]S. Beigi and R. Knig, New J. Phys. 13 , 093036 (2011). http://dx.doi.org/10.1088/1367-2630/13/9/093036 · DOI
  3. [33]H. Bomb´ ın, New J. Phys. 17 , 083002 (2015). http://dx.doi.org/10.1088/1367-2630/17/8/083002 · DOI · Paper page
  4. [35]R. Kueng, D. M. Long, A. C. Doherty, and S. T. Flammia, arXiv:1510.05653 [quant-ph]. · arXiv
  5. [36][J. J. Wallman, arXiv:1511.00727 [quant-ph].](http://arxiv.org/abs/1511.00727) · arXiv
  6. [38]L. Viola and E. Knill, Phys. Rev. Lett. 94 , 060502 (2005). http://dx.doi.org/10.1103/PhysRevLett.94.060502 · DOI · Paper page

Cited by

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Authors
Wallman, J. J., & Emerson, J.
Affiliations
University of Waterloo (CA)
ORCID
Venue
Physical Review A
Publisher
American Physical Society (APS)
Published
2016-11-18
Volume
94
Issue
5
ISSN
  • 0556-2791 (ISSN-L)
  • 2469-9926
  • 2469-9934
DOI
10.1103/physreva.94.052325
OpenAlex
W2268604949
Cited by
535
References
8
Citations by year
2026: 65 · 2025: 129 · 2024: 100 · 2023: 66 · 2022: 54 · 2021: 63 · 2020: 25 · 2019: 16 · 2018: 8 · 2017: 6 · 2016: 2 · 2015: 1
FWCI
8.78
Type
journal article
Language
en
Open access
Licence
Locations
  • Physical Review A (publishedVersion)
  • arXiv (Cornell University) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Army Research Office (W911NF-14-1-0103)
  • Canadian Institute for Advanced Research
  • Natural Sciences and Engineering Research Council of Canada
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
fault-tolerant quantum computing, randomized benchmarking, gate fidelity, scalable quantum computing, coherent noise

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