Quantifying the effects of local many-qubit errors and nonlocal two-qubit errors on the surface code
Open accessAbstract
Topological quantum error correction codes are known to be able to tolerate arbitrary local errors given sufficient qubits. This includes correlated errors involving many local qubits. In this work, we quantify this level of tolerance, numerically studying the effects of many-qubit errors on the performance of the surface code. We find that if increasingly large-area errors are at least moderately exponentially suppressed, arbitrarily reliable quantum computation can still be achieved with practical overhead. We furthermore quantify the effect of nonlocal two-qubit correlated errors, which would be expected in arrays of qubits coupled by a polynomially decaying interaction, and when using many-qubit coupling devices. We surprisingly find that the surface code is very robust to this class of errors, despite a provable lack of a threshold error rate when such errors are present.
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A correlated error event affecting many qubits simultaneously is a recipe for logical faults.
“A correlated error event is particularly problematic, as a ecting many qubits simultaneously is a recipe for logical faults [6].”
From Resolving catastrophic error bursts from cosmic rays in large arrays of superconducting qubits (2022) · cites this paper as [6]
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Cites
Non-Abelian anyons and topological quantum computation
Nayak, C., Simon, S. H., Stern, A., Freedman, M., & Das Sarma, S. (2008) · Reviews of Modern Physics · doi:10.1103/revmodphys.80.1083 · Cited by 6,861 · see citing works
Quantum computation with quantum dots
Loss, D., & DiVincenzo, D. P. (1998) · Physical Review A · doi:10.1103/physreva.57.120 · Cited by 6,840 · see citing works
Surface codes: Towards practical large-scale quantum computation
Fowler, A. G., Mariantoni, M., Martinis, J. M., & Cleland, A. N. (2012) · Physical Review A · doi:10.1103/physreva.86.032324 · Cited by 3,059 · see citing works
Self-citationThe Zeno’s paradox in quantum theory
Misra, B., & Sudarshan, E. C. G. (1977) · Journal of Mathematical Physics · doi:10.1063/1.523304 · Cited by 2,246 · see citing works
Architecture for a large-scale ion-trap quantum computer
Kielpinski, D., Monroe, C., & Wineland, D. J. (2002) · Nature · doi:10.1038/nature00784 · Cited by 1,589 · see citing works
Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions
Raussendorf, R., & Harrington, J. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.190504 · Cited by 812 · see citing works
Coherent Josephson Qubit Suitable for Scalable Quantum Integrated Circuits
Barends, R., Kelly, J., Megrant, A., Sank, D., Jeffrey, E., Chen, Y., Yin, Y., Chiaro, B., Mutus, J., Neill, C., et al. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.080502 · Cited by 779 · see citing works
Self-citationQuantum Logic Gates in Optical Lattices
Brennen, G. K., Caves, C. M., Jessen, P., & Deutsch, I. (1999) · Physical Review Letters · doi:10.1103/physrevlett.82.1060 · Cited by 659 · see citing works
Topological fault-tolerance in cluster state quantum computation
Raussendorf, R., Harrington, J., & Goyal, K. (2007) · New Journal of Physics · doi:10.1088/1367-2630/9/6/199 · Cited by 617 · see citing works
Two-dimensional architectures for donor-based quantum computing
Hollenberg, L. C. L., Greentree, A. D., Fowler, A. G., & Wellard, C. J. (2006) · Physical Review B · doi:10.1103/physrevb.74.045311 · Cited by 258 · see citing works
Self-citationFault-Tolerant Quantum Computation with Long-Range Correlated Noise
Aharonov, D., Kitaev, A., & Preskill, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.050504 · Cited by 243 · see citing works
Toward fault-tolerant quantum computation without concatenation
Dennis, E. (2001) · Physical Review A · doi:10.1103/physreva.63.052314 · Cited by 72 · see citing works
Fault-tolerant quantum computation versus Gaussian noise
Ng, H. K., & Preskill, J. P. (2009) · Physical Review A · doi:10.1103/physreva.79.032318 · Cited by 64 · see citing works
Quantum circuits for measuring Levin-Wen operators
Bonesteel, N. E., & Divincenzo, D. P. (2012) · Physical Review B · doi:10.1103/physrevb.86.165113 · Cited by 37 · see citing works
Flagged first, then by citations
Research works printed but not linked: 14
- [2]N. E. Bonesteel and D. P. DiVincenzo, Phys. Rev. B 86 , 165113 (2012), arXiv:1206.6048. · arXiv
- [3]D. Gottesman, arXiv:1310.2984 (2013). · arXiv
- [4]H. Bombin, arXiv:1311.0879 (2013). · arXiv
- [5]S. Bravyi and M. B. Hastings, arXiv:1311.0885 (2013). · arXiv
- [6]S. B. Bravyi and A. Y. Kitaev, quant-ph/9811052 (1998). · arXiv
- [8]R. Raussendorf and J. Harrington, Phys. Rev. Lett. 98 , 190504 (2007), quant-ph/0610082. · arXiv
- [9]R. Raussendorf, J. Harrington, and K. Goyal, New J. Phys. 9 , 199 (2007), quant-ph/0703143. · arXiv
- [10]A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Phys. Rev. A 86 , 032324 (2012), arXiv:1208.0928. · arXiv
- [12]D. Aharonov, A. Kitaev, and J. Preskill, Phys. Rev. Lett. 96 , 050504 (2006), quant-ph/0510231. · arXiv
- [13]H. K. Ng and J. Preskill, Phys. Rev. A 79 , 032318 (2009), arXiv:0810.4953. · arXiv
- [14]J. Preskill, Quant. Inf. Comput. 13 , 181 (2013), arXiv:1207.6131. · arXiv
- [15]R. Barends, J. Kelly, A. Megrant, D. Sank, E. Jeffrey, Y. Chen, Y. Yin, B. Chiaro, J. Mutus, C. Neill, P. O'Malley, P. Roushan, J. Wenner, T. C. White, A. N. Cleland, and J. M. Martinis, Phys. Rev. Lett. 111 , 080502 (2013), arXiv:1304.2322. · arXiv
- [17]D. Loss and D. P. DiVincenzo, Phys. Rev. A 57 , 120 (1998), cond-mat/9701055. · arXiv
- [21]A. G. Fowler, arXiv:1310.0863 (2013). · arXiv
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- Authors
- Fowler, A. G., & Martinis, J. M.
- Affiliations
- University of California, Santa Barbara (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2014-03-12
- Volume
- 89
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2143142748
- Cited by
- 49
- References
- 14
- Citations by year
- 2026: 1 · 2025: 9 · 2024: 3 · 2023: 5 · 2022: 2 · 2021: 7 · 2020: 1 · 2019: 4 · 2018: 2 · 2017: 2 · 2016: 4 · 2015: 5 · 2014: 4
- FWCI
- 4.99
- 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 many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Keywords
- surface code, topological quantum error correction, correlated errors, error tolerance, error threshold, qubit coupling, fault tolerance
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