The DOI matches its Crossref record; 52 of the 52 references it cites were found in a registry or an index.
Fault-tolerant thresholds for quantum error correction with the surface code
Open accessAbstract
The surface code is a promising candidate for fault-tolerant quantum computation, achieving a high threshold error rate with nearest-neighbor gates in two spatial dimensions. Here, through a series of numerical simulations, we investigate how the precise value of the threshold depends on the noise model, measurement circuits, and decoding algorithm. We observe thresholds between 0.502(1)% and 1.140(1)% per gate, values which are generally lower than previous estimates.
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“This threshold behaviour can be subtle58, and there exists a crossover regime in which, owing to finite-size effects, increasing system size initially suppresses the logical error per cycle before later increasing it.”
From Suppressing quantum errors by scaling a surface code logical qubit (2023) · cites this paper as [58]
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Citations
Cites
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Flagged first, then by citations
Research works printed but not linked: 7
- P. Aliferis, 2006, Quantum Inf. Comput., 6, 97
- D. Aharonov, 1998, Proceedings of the 29th Annual ACM Symposium on the Theory of Computation
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“04) ± % , a level consistent with estimates of error thresholds needed for fault tolerance [39, 40].”
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Chai, J. H., & Ng, H. K. (2022) · Advanced Quantum Technologies · doi:10.1002/qute.202200008 · Cited by 2
Logical qubit behavior model and fast simulation for surface code
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Heng, S., Heng, S., Kim, D., & Han, Y. (2024) · Physical Review A · doi:10.1103/physreva.109.022440 · Cited by 1
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Mezzadri, M., Chiesa, A., Lepori, L., & Carretta, S. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2307.10761 · Cited by 1
“Yet, a comprehensive Fault-Tolerant implementation accommodating realistic noise models, which encompass noisy ancillae, encodings, measurements and especially noise during gates, is still missing [23, 36].”
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Freeman, C. D. (2018) · eScholarship (California Digital Library)
Classical Control of Large-Scale Quantum ComputersPreprint
Devitt, S. J. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1405.4943
“This can reduce the amount of information as the probability that a unit cell of the lattice will experience a parity flip is of the order of the error rate of each qubit, p , which will be approximately 0.1% [48].”
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Al-Hinai, M., & Asif, H. M. (2025) · IEEE Asia Pacific Conference on Wireless and Mobile (APWiMob) · doi:10.1109/apwimob67231.2025.11269136
“By contrast, the Steane code shows higher fluctuations, leading to wider CI bands and demonstrating weaker resilience to noise None of the tested QECCs exhibited a clear pseudo-threshold crossing at their original code distances [26].”
Shkolnik, G., Gopalakrishnan, S., Huse, D. A., Gazit, S., & Pixley, J. H. (2025) · Physical review. B./Physical review. B · doi:10.1103/nq1j-7tzg
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Generalized code distance through rotated logical states in quantum error correction
Nyirahafashimana, V., Shah, N. M., Halim, U. A., & Othman, M. (2026) · Theoretical Computer Science · doi:10.1016/j.tcs.2026.115795
“For sufficiently large d R , the p R log is expected to follow the relation: where ν 0 denotes the scaling exponent associated with the universality class of the SD and SI noise model [10].”
InfluentialReinforcement learning-based topological $$\textrm{XYZ}^{2}$$ lattice transformation decoding
Li, A., Li, F., Guo, X., Zhang, Y., Liang, J., & Ma, H. (2026) · Quantum Information Processing · doi:10.1007/s11128-026-05063-x
“As shown in the figure, X , Y , and Z errors generate syndromes along their respective unique directions, similar to surface code errors on a square lattice [38–40].”
Fault-tolerant threshold of quantum circuit under correlated noise
Wang, Z.-Y. (2026) · Communications in Theoretical Physics · doi:10.1088/1572-9494/ae4b15
“It is highly dependent on the specific quantum hardware platform, the choice of error-correcting code [ 19–22 ] , and the underlying noise model [ 23, 24 ] .”
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Wang, X., Huang, C., & Fan, X. (2026) · Applied Sciences · doi:10.3390/app16115409
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Chen, Z., Cai, K., Cen, W., Zhang, J., & Ye, J. (2026) · IEEE Conference on Computer Communications (INFOCOM) · doi:10.1109/infocom59046.2026.11571406
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“75% using the finite-size scaling ansatz [61, 62], which is comparable to the MWPM decoding threshold for toric and surface codes [13,14,63,64], estimated to be roughly 0.75%–1%.”
InfluentialChancellor, N. (2017) · Durham Research Online (Durham University) · doi:10.15128/r1bn999672k
Metadata
- Authors
- Stephens, A. M.
- Affiliations
- National Institute of Informatics (JP)
- Corresponding author
- Stephens, Ashley M.
- ORCID
- Stephens, Ashley M.
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2014-02-14
- Volume
- 89
- Issue
- 2
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2044503188
- Cited by
- 133
- References
- 52
- Citations by year
- 2026: 13 · 2025: 11 · 2024: 15 · 2023: 17 · 2022: 17 · 2021: 8 · 2020: 7 · 2019: 4 · 2018: 11 · 2017: 12 · 2016: 4 · 2015: 6 · 2014: 8
- FWCI
- 9.88
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Keywords
- surface code, fault-tolerant quantum computing, error threshold, quantum error correction, noise models, measurement circuit, decoding algorithms
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