Flag fault-tolerant error correction with arbitrary distance codes
Open accessAbstract
In this paper we introduce a general fault-tolerant quantum error correction protocol using flag circuits for measuring stabilizers of arbitrary distance codes. In addition to extending flag error correction beyond distance-three codes for the first time, our protocol also applies to a broader class of distance-three codes than was previously known. Flag circuits use extra ancilla qubits to signal when errors resulting from v faults in the circuit have weight greater than v . The flag error correction protocol is applicable to stabilizer codes of arbitrary distance which satisfy a set of conditions and uses fewer qubits than other schemes such as Shor, Steane and Knill error correction. We give examples of infinite code families which satisfy these conditions and analyze the behaviour of distance-three and -five examples numerically. Requiring fewer resources than Shor error correction, flag error correction could potentially be used in low-overhead fault-tolerant error correction protocols using low density parity check quantum codes of large code length.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
To detect errors and perform corrections, often additional auxiliary qubits are used, increasing the actual number of physical qubits required for QEC.
“To detect errors and perform corrections, often additional auxiliary qubits are being used.Thus, the actual number of physical qubits required for QEC is increased further [59,60].”
From Neutral atom quantum computing hardware: performance and end-user perspective (2023) · cites this paper as [59]
Cites
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 · cited 1× · see citing works
“As was shown in [9], CNOT gate failures have the largest impact on the pseudo-threshold of the surface code.”
BackgroundGood quantum error-correcting codes exist
Calderbank, A. R., & Shor, P. W. (1996) · Physical Review A · doi:10.1103/physreva.54.1098 · Cited by 2,516 · see citing works
Edmonds, J. (1965) · Canadian Journal of Mathematics · doi:10.4153/cjm-1965-045-4 · Cited by 2,428 · see citing works
Quantum error correction for quantum memories
Terhal, B. M. (2015) · Reviews of Modern Physics · doi:10.1103/revmodphys.87.307 · Cited by 1,354 · see citing works
Quantum computing with realistically noisy devices
Knill, E. (2005) · Nature · doi:10.1038/nature03350 · Cited by 1,184 · cited 1× · see citing works
“Knill EC typically achieves higher thresholds than Shor and Steane EC but often uses more qubits [20, 21].”
BackgroundSubsystem Fault Tolerance with the Bacon-Shor Code
Aliferis, P., & Cross, A. W. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.220502 · Cited by 203 · see citing works
Fault-Tolerant quantum computation with constant overhead
Gottesman, D. (2014) · Quantum Information and Computation · doi:10.26421/qic14.15-16-5 · Cited by 172 · see citing works
Optimal and efficient decoding of concatenated quantum block codes
Poulin, D. (2006) · Physical Review A · doi:10.1103/physreva.74.052333 · Cited by 105 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Demonstration of fault-tolerant universal quantum gate operations
Postler, L., Heuβen, S., Pogorelov, I., Rispler, M., Feldker, T., Meth, M., Marciniak, C. D., Stricker, R., Ringbauer, M., Blatt, R., et al. (2022) · Nature · doi:10.1038/s41586-022-04721-1 · Cited by 287 · see citing works
Building a Fault-Tolerant Quantum Computer Using Concatenated Cat Codes
Chamberland, C., Noh, K., Arrangoiz-Arriola, P., Campbell, E. T., Hann, C. T., Iverson, J., Putterman, H., Bohdanowicz, T. C., Flammia, S. T., Keller, A., et al. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010329 · Cited by 281 · see citing works
Self-citationTopological and Subsystem Codes on Low-Degree Graphs with Flag Qubits
Chamberland, C., Zhu, G., Yoder, T. J., Hertzberg, J. B., & Cross, A. W. (2020) · Physical Review X · doi:10.1103/physrevx.10.011022 · Cited by 223 · see citing works
Self-citationNeutral atom quantum computing hardware: performance and end-user perspective
Wintersperger, K., Dommert, F., Ehmer, T., Hoursanov, A., Klepsch, J., Mauerer, W., Reuber, G., Strohm, T., Yin, M., & Luber, S. (2023) · EPJ Quantum Technology · doi:10.1140/epjqt/s40507-023-00190-1 · Cited by 117 · see citing works
Encoding a magic state with beyond break-even fidelity
Gupta, R. S., Sundaresan, N., Alexander, T., Wood, C. J., Merkel, S. T., Healy, M. B., Hillenbrand, M., Jochym-O’Connor, T., Wootton, J. R., Yoder, T. J., et al. (2024) · Nature · doi:10.1038/s41586-023-06846-3 · Cited by 115 · see citing works
Triangular color codes on trivalent graphs with flag qubits
Chamberland, C., Kubica, A., Yoder, T. J., & Zhu, G. (2020) · New Journal of Physics · doi:10.1088/1367-2630/ab68fd · Cited by 105 · see citing works
Self-citationDemonstration of Fault-Tolerant Steane Quantum Error Correction
Postler, L., Butt, F., Pogorelov, I., Marciniak, C. D., Heußen, S., Blatt, R., Schindler, P., Rispler, M., Müller, M., & Monz, T. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.030326 · Cited by 66 · see citing works
Error rates and resource overheads of repetition cat qubits
Guillaud, J., & Mirrahimi, M. (2021) · Physical Review A · doi:10.1103/physreva.103.042413 · Cited by 55 · see citing works
Improving Threshold for Fault-Tolerant Color-Code Quantum Computing by Flagged Weight Optimization
Takada, Y., & Fujii, K. (2024) · PRX Quantum · doi:10.1103/prxquantum.5.030352 · Cited by 10 · see citing works
- Authors
- Chamberland, C., & Beverland, M. E.
- Affiliations
- University of Waterloo (CA)
- Microsoft (United States) (US)
- Venue
- Quantum
- Published
- 2018-02-08
- Volume
- 2
- Pages
- 53
- ISSN
- 2521-327X (ISSN-L)
- OpenAlex
- W2744938842
- Cited by
- 159
- References
- 8
- Citations by year
- 2026: 13 · 2025: 26 · 2024: 25 · 2023: 18 · 2022: 18 · 2021: 19 · 2020: 17 · 2019: 13 · 2018: 9 · 2017: 1
- FWCI
- 8.16
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- Quantum (publishedVersion, cc-by)
- arXiv (Cornell University) (acceptedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- arXiv (Cornell University) (cc-by)
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Coding theory and cryptography
- Keywords
- fault-tolerant quantum error correction, stabilizer codes, ancilla qubits, LDPC codes, quantum error-correcting codes
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
