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Cited by 5Quantum Computing Algorithms and ArchitectureQuantum many-body systemsQuantum Information and Cryptography

Quantum error correction with an Ising machine under circuit-level noise

Open access
Fujisaki, Jun, Maruyama, Kazunori, Oshima, Hirotaka, Sato, Shintaro, Sakashita, Tatsuya, Takeuchi, Yusaku, Fujii, Keisuke·2023·Physical Review Research
DOI 10.1103/physrevresearch.5.043261
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Abstract

Efficient decoding to estimate error locations from outcomes of syndrome measurements is the prerequisite for quantum error correction. Decoding in the presence of circuit-level noise including measurement errors should be considered in case of actual quantum computing devices. In this paper, we develop a decoder for circuit-level noise that solves the error estimation problems as Ising-type optimization problems. We confirm that the threshold theorem in the surface code under circuit-level noise is reproduced with an error threshold of approximately 0.4%. We also demonstrate the advantage of the decoder through which the $Y$ error detection rate can be improved compared with other matching-based decoders. Our results reveal that a lower logical error rate can be obtained using our algorithm compared with that of the minimum-weight perfect matching algorithm.

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  • MLE can be mapped to a quadratic unconstrained binary optimization (QUBO) problem.

    “In particular, one first maps MLE to a quadratic unconstrained binary optimization (QUBO) problem [213–215].”

    From Quantum error correction and fault tolerance: A comprehensive tutorial (2026) · cites this paper as [214]

    Section II and Appendix B describe mapping a quantum-error-correction decoding cost function into QUBO form. They do not identify that cost function as maximum likelihood estimation (MLE) or establish a general mapping from MLE to QUBO; searches for “maximum likelihood” and “MLE” found no such passage. No page numbers are available in our copy. (LLM, conf=0.78)

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Authors
Fujisaki, J., Maruyama, K., Oshima, H., Sato, S., Sakashita, T., Takeuchi, Y., & Fujii, K.
Affiliations
  • Fujitsu (Japan) (JP)
  • Center for Quantum Information and Quantum Biology, The University of Osaka (JP)
  • RIKEN Center for Quantum Computing (JP)
ORCID
Venue
Physical Review Research
Publisher
American Physical Society (APS)
Published
2023-12-19
Volume
5
Issue
4
ISSN
2643-1564 (ISSN-L)
DOI
10.1103/physrevresearch.5.043261
OpenAlex
W4389936051
Cited by
5
References
37
Citations by year
2026: 1 · 2025: 3 · 2024: 1
FWCI
0.47
Type
journal article
Language
en
Update notices
correction (2024-02-07)
Open access
Licence
Locations
  • Physical Review Research (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • arXiv (Cornell University)
Funders
  • Ministry of Education, Culture, Sports, Science and Technology (JPMXS0118067394, JPMXS0120319794)
  • Japan Science and Technology Agency (JPMJPF2014, JPMJMS2061)
Topics
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
  • Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
Keywords
quantum error correction, Ising machines, error decoding, surface code, threshold theorem, measurement error, minimum-weight perfect matching, logical error rate, syndrome measurement

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