Subsystem Fault Tolerance with the Bacon-Shor Code
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We discuss how the presence of gauge subsystems in the Bacon-Shor code [D. Bacon, Phys. Rev. A 73, 012340 (2006)10.1103/PhysRevA.73.012340 (2006)] leads to remarkably simple and efficient methods for fault-tolerant error correction (FTEC). Most notably, FTEC does not require entangled ancillary states, and it can be implemented with nearest-neighbor two-qubit measurements. By using these methods, we prove a lower bound on the quantum accuracy threshold, 1.94 x 10(-4) for adversarial stochastic noise, that improves previous lower bounds by nearly an order of magnitude.
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Calderbank and Shor and Steane showed that good quantum error-correcting codes exist.
“Immediately after that, Calderbank and Shor[13] and Steane[68] showed that good quantum error correcting codes exist”
From Fault-Tolerant Quantum Computation with Constant Error Rate (2008) · cites this paper as [13]
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Bény, C., Kempf, A., & Kribs, D. W. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3155783 · Cited by 20 · see citing works
Optimized measurement-free and fault-tolerant quantum error correction for neutral atoms
Veroni, S., Müller, M., & Giudice, G. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.043253 · Cited by 19 · see citing works
Continuous quantum error correction for evolution under time-dependent Hamiltonians
Atalaya, J., Zhang, S., Niu, M. Y., Babakhani, A., Chan, C. H. H., Epstein, J. M., & Whaley, K. B. (2021) · Physical Review A · doi:10.1103/physreva.103.042406 · Cited by 19 · see citing works
Error-Detection-Based Quantum Fault-Tolerance Threshold
Reichardt, B. W. (2007) · Algorithmica · doi:10.1007/s00453-007-9069-7 · Cited by 17 · see citing works
Scheme for fault-tolerant holonomic computation on stabilizer codes
Oreshkov, O., Brun, T. A., & Lidar, D. A. (2009) · Physical Review A · doi:10.1103/physreva.80.022325 · Cited by 16 · see citing works
- Authors
- Aliferis, P., & Cross, A. W.
- Affiliations
- California Institute of Technology (US)
- IBM Research - Thomas J. Watson Research Center (US)
- ORCID
- Cross, Andrew W.
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2007-05-31
- Volume
- 98
- Issue
- 22
- Pages
- 220502-220502
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W1974123702
- Cited by
- 203
- References
- 14
- Citations by year
- 2026: 4 · 2025: 13 · 2024: 11 · 2023: 10 · 2022: 8 · 2021: 11 · 2020: 12 · 2019: 9 · 2018: 10 · 2017: 9 · 2016: 9 · 2015: 5 · 2014: 5 · 2013: 14 · 2012: 13
- FWCI
- 18.13
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CaltechAUTHORS (California Institute of Technology) (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
- Bacon-Shor code, quantum error correction, lower bounds, adversarial perturbations
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