The DOI matches its Crossref record; 14 of the 14 references it cites were found in a registry or an index.
Subsystem Fault Tolerance with the Bacon-Shor Code
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
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?
In the citing paper
“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]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Scheme for reducing decoherence in quantum computer memory
Shor, P. W. (1995) · Physical Review A · doi:10.1103/physreva.52.r2493 · Cited by 4,479
Quantum computing with realistically noisy devices
Knill, E. (2005) · Nature · doi:10.1038/nature03350 · Cited by 1,184
Theory of Quantum Error Correction for General Noise
Knill, E., Laflamme, R., & Viola, L. (2000) · Physical Review Letters · doi:10.1103/physrevlett.84.2525 · Cited by 866
Operator quantum error-correcting subsystems for self-correcting quantum memories
Bacon, D. (2006) · Physical Review A · doi:10.1103/physreva.73.012340 · Cited by 486
Quantum accuracy threshold for concatenated distance-3 code
Aliferis, P., Gottesman, D., & Preskill, J. (2006) · Quantum Information and Computation · doi:10.26421/qic6.2-1 · Cited by 412
Self-citationStabilizer Formalism for Operator Quantum Error Correction
Poulin, D. (2005) · Physical Review Letters · doi:10.1103/physrevlett.95.230504 · Cited by 375
Active Stabilization, Quantum Computation, and Quantum State Synthesis
Steane, A. M. (1997) · Physical Review Letters · doi:10.1103/physrevlett.78.2252 · Cited by 308
Proc. 26th annual symposium on Foundations of computer science
Tarjan, R. E. (1985) · Cited by 258
Fault-tolerant quantum computation for local non-Markovian noise
Terhal, B. M., & Burkard, G. (2005) · Physical Review A · doi:10.1103/physreva.71.012336 · Cited by 191
Operator quantum error correction
Kribs, D. W., & Poulin, D. (2013) · Cambridge University Press eBooks · doi:10.1017/cbo9781139034807.008 · Cited by 102
Flagged first, then by citations
Cited by
Sorted by citations
Items 101–200 of 203
Design of nanophotonic circuits for autonomous subsystem quantum error correctionPreprint
Kerckhoff, J., Pavlichin, D. S., Chalabi, H., & Mabuchi, H. (2011) · Cited by 18
Sparse Quantum Codes from Quantum Circuits
Bacon, D., Flammia, S. T., Harrow, A. W., & Shi, J. (2015) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/2746539.2746608 · Cited by 17
Error-correcting Bacon-Shor code with continuous measurement of noncommuting operators
Atalaya, J., Korotkov, A. N., & Whaley, K. B. (2020) · Physical Review A · doi:10.1103/physreva.102.022415 · Cited by 16
Stability of quantum concatenated-code Hamiltonians
Bacon, D. (2008) · Physical Review A · doi:10.1103/physreva.78.042324 · Cited by 17
Ziegler, L., Tirrito, E., Lewenstein, M., Hands, S., & Bermúdez, A. (2022) · Annals of Physics · doi:10.1016/j.aop.2022.168763 · Cited by 17
Nonlocal quantum information in bipartite quantum error correction
Wilde, M. M., & Fattal, D. A. (2010) · Quantum Information Processing · doi:10.1007/s11128-010-0175-0 · Cited by 16
Huang, S., & Brown, K. R. (2020) · Physical Review A · doi:10.1103/physreva.101.042312 · Cited by 19
Practical fault tolerance for quantum circuits
Kubiatowicz, J. D., & Whitney, M. (2009) · Cited by 15
Lai, C., Zheng, Y.-C., & Brun, T. A. (2017) · Physical Review A · doi:10.1103/physreva.95.032339 · Cited by 17
Topological subsystem codes from graphs and hypergraphs
Sarvepalli, P. K., & Brown, K. R. (2012) · Physical Review A · doi:10.1103/physreva.86.042336 · Cited by 15
Comparative study of quantum error correction strategies for the heavy-hexagonal lattice
Benito, C., López, E., Peropadre, B., & Bermúdez, A. (2025) · Quantum · doi:10.22331/q-2025-02-06-1623 · Cited by 26
Benchmarking quantum logic operations relative to thresholds for fault tolerance
Hashim, A., Seritan, S., Proctor, T. J., Rudinger, K., Goss, N., Naik, R., Kreikebaum, J. M., Santiago, D., & Siddiqi, I. A. (2023) · npj Quantum Information · doi:10.1038/s41534-023-00764-y · Cited by 23
Dynamical decoupling of a qubit with always-on control fields
Jones, N. C., Ladd, T. D., & Fong, B. H. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/9/093045 · Cited by 16
Logic Synthesis for Fault-Tolerant Quantum ComputersPreprint
Jones, N. C. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1310.7290 · Cited by 18
QUANTUM ERROR CORRECTION ON INFINITE-DIMENSIONAL HILBERT SPACESPreprint
Bény, C., Kempf, A., Kribs, D. W., & Kribs, W. (2012) · Cited by 18
Leveraging automorphisms of quantum codes for fault-tolerant quantum computation
Grassl, M., & Roetteler, M. (2013) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit.2013.6620283 · Cited by 13
Efficient preparation of large-block-code ancilla states for fault-tolerant quantum computation
Zheng, Y.-C., Lai, C., & Brun, T. A. (2018) · Physical Review A · doi:10.1103/physreva.97.032331 · Cited by 14
CONSTRUCTIONS OF OPTIMAL SUBSYSTEM CODES
Qian, J., & Zhang, L. (2012) · Modern Physics Letters B · doi:10.1142/s0217984912501734 · Cited by 12
Homological Quantum Rotor Codes: Logical Qubits from Torsion
Vuillot, C., Ciani, A., & Terhal, B. M. (2024) · Communications in Mathematical Physics · doi:10.1007/s00220-023-04905-4 · Cited by 21
Quantum computation with doped silicon cavities
Abanto, M., Davidovich, L., Koiller, B., & Filho, R. L. D. M. (2010) · Physical Review B · doi:10.1103/physrevb.81.085325 · Cited by 12
Nonlocal quantum information in bipartite quantum error correction
Wilde, M. M., & Fattal, D. A. (2010) · Civil War Book Review · Cited by 11
Optimal quantum subsystem codes in two dimensions
Yoder, T. J. (2019) · Physical Review A · doi:10.1103/physreva.99.052333 · Cited by 11
Density matrix simulation of quantum error correction codes for near-term quantum devices
Baek, C., Ostuka, T., Tarucha, S., & Choi, B.-S. (2019) · Quantum Science and Technology · doi:10.1088/2058-9565/ab5887 · Cited by 12
Convolutional-Neural-Network-Based Hexagonal Quantum Error Correction Decoder
Li, A.-Q., Li, F., Qi-Di, G. A. N., & Ma, H. (2023) · Applied Sciences · doi:10.3390/app13179689 · Cited by 12
Performance and error analysis of Knill's postselection scheme in a two-dimensional architecture
Lai, C., Paz-Silva, G. A., Suchara, M., & Brun, T. A. (2014) · Quantum Information and Computation · doi:10.26421/qic14.9-10-7 · Cited by 10
Raman sideband cooling of a Ba+138 ion using a Zeeman interval
Seck, C. M., Kokish, M., Dietrich, M., & Odom, B. (2016) · Physical Review A · doi:10.1103/physreva.93.053415 · Cited by 9
Parameter regimes for surpassing the PLOB bound with error-corrected qudit repeaters
Miller, D., Holz, T., Kampermann, H., & Bruß, D. (2019) · Quantum · doi:10.22331/q-2019-12-16-216 · Cited by 9
Gauge subsystems, separability and robustness in autonomous quantum memories
Sarma, G., & Mabuchi, H. (2013) · New Journal of Physics · doi:10.1088/1367-2630/15/3/035014 · Cited by 10
Optimal correction of concatenated fault-tolerant quantum codes
Evans, Z. W. E., & Stephens, A. M. (2011) · Quantum Information Processing · doi:10.1007/s11128-011-0312-4 · Cited by 12
Robustness of operator quantum error correction with respect to initialization errors
Oreshkov, O. (2008) · Physical Review A · doi:10.1103/physreva.77.032333 · Cited by 10
Analytical error analysis of Clifford gates by the fault-path tracer method
Janardan, S., Tomita, Y., Gutiérrez, M., & Brown, K. R. (2016) · Quantum Information Processing · doi:10.1007/s11128-016-1330-z · Cited by 11
Asymmetric and Symmetric Subsystem BCH Codes and BeyondPreprint
Aly, S. A. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0803.0764 · Cited by 9
Some constructions of optimal subsystem codes derived from GRS codes
Wang, G., & Tang, C. (2022) · Quantum Information Processing · doi:10.1007/s11128-022-03622-6 · Cited by 9
Magic state distillation and cost analysis in fault-tolerant universal quantum computation
Liu, Y., Ma, Z., Luo, L., Du, C., Fei, Y., Wang, H., Duan, Q., & Yang, J. (2023) · Quantum Science and Technology · doi:10.1088/2058-9565/ace6ca · Cited by 9
Quantum computer error structure probed by quantum error correction syndrome measurements
Gicev, S., Hollenberg, L. C. L., & Usman, M. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.043249 · Cited by 14
Scalable quantum computation with fast gates in two-dimensional microtrap arrays of trapped ions
Mehdi, Z., Ratcliffe, A. K., & Hope, J. J. (2020) · Physical Review A · doi:10.1103/physreva.102.012618 · Cited by 9
Quantum subsystem codes, CFTs and their ℤ2-gaugings
Ando, K., Kawabata, K., & Nishioka, T. (2024) · Journal of High Energy Physics · doi:10.1007/jhep11(2024)125 · Cited by 13
Quantum-error-correction benchmarks for continuous weak-parity measurements
Denhez, G., Blais, A., & Poulin, D. (2012) · Physical Review A · doi:10.1103/physreva.86.032318 · Cited by 8
Message passing in fault-tolerant quantum error correction
Evans, Z. W. E., & Stephens, A. M. (2008) · Physical Review A · doi:10.1103/physreva.78.062317 · Cited by 8
Floquet analysis of frequency collisions
Heya, K., Malekakhlagh, M., Merkel, S., Kanazawa, N., & Pritchett, E. (2024) · Physical Review Applied · doi:10.1103/physrevapplied.21.024035 · Cited by 10
Dissipative encoding of quantum information
Baggio, G., Ticozzi, F., Johnson, P. D., & Viola, L. (2021) · Quantum Information and Computation · doi:10.26421/qic21.9-10-2 · Cited by 9
The idiots guide to Quantum Error CorrectionPreprint
Devitt, S. J., Nemoto, K., & Munro, W. J. (2009) · arXiv (Cornell University) · Cited by 7
On Quantum and Classical Error Control Codes: Constructions and ApplicationsPreprint
Aly, S. A. (2008) · arXiv (Cornell University) · doi:10.48550/arxiv.0812.5104 · Cited by 7
Quantum Error Correction with Biased Noise
Brooks, P. (2013) · CaltechTHESIS (California Institute of Technology) · doi:10.7907/1tvt-j780 · Cited by 7
Operator Algebraic Formulation of the Stabilizer Formalism for Quantum Error Correction
Johnston, N., Kribs, D. W., & Teng, C.-W. (2009) · Acta Applicandae Mathematicae · doi:10.1007/s10440-008-9421-1 · Cited by 6
Reliable Channel-Adapted Error Correction: Bacon-Shor Code Recovery from Amplitude Damping
Piedrafita, Á., & Renes, J. M. (2017) · Physical Review Letters · doi:10.1103/physrevlett.119.250501 · Cited by 6
Superconducting and Silicon-Based Semiconductor Quantum Computers: A review
Jia, Z.-L., Fu, Y., Cao, Z. X., Cheng, W., Zhao, Y., Dou, M., Duan, P., Kong, W., Cao, G., Li, H.-O., et al. (2022) · IEEE Nanotechnology Magazine · doi:10.1109/mnano.2022.3175394 · Cited by 5
Zhang, Y., Liu, Y., Hou, X., & Gao, J. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04013-1 · Cited by 5
Automated searching for quantum subsystem codes
Crosswhite, G. M., & Bacon, D. (2011) · Physical Review A · doi:10.1103/physreva.83.022307 · Cited by 5
Fault-tolerant quantum computer architectures using hierarchies of quantum error-correcting codes
Chuang, I. L., & Cross, A. W. (2008) · Cited by 7
Self-citationUniversal Quantum Computation via Scalable Measurement-Free Error Correction
Veroni, S., Paler, A., & Giudice, G. (2025) · PRX Quantum · doi:10.1103/lkk1-v6wp · Cited by 11
Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
Escobar-Arrieta, G., & Gutiérrez, M. (2025) · Physical Review A · doi:10.1103/physreva.111.032427 · Cited by 6
Manipulation of NOT gate in Non-Markovian open quantum systems
Liu, J., & Cong, S. (2014) · World Congress on Intelligent Control and Automation · doi:10.1109/wcica.2014.7052895 · Cited by 4
QuCirDET: A design and simulation tool for quantum circuits
Prousalis, K. P., & Konofaos, N. (2016) · International Conference on Modern Circuits and Systems Technologies · doi:10.1109/mocast.2016.7495162 · Cited by 4
Two-qubit sweet spots for capacitively coupled exchange-only spin qubits
Feng, M., Zaw, L. H., & Koh, T. S. (2021) · npj Quantum Information · doi:10.1038/s41534-021-00449-4 · Cited by 4
Quantum Teleportation in the Commuting Operator Framework
Conlon, A., Crann, J., Kribs, D. W., & Levene, R. H. (2022) · Annales Henri Poincaré · doi:10.1007/s00023-022-01255-0 · Cited by 4
Surface code for low-density qubit array
Tomaru, T., Yoshimura, C., & Mizuno, H. (2022) · Scientific Reports · doi:10.1038/s41598-022-17090-6 · Cited by 5
Stabilizer subsystem codes with spatially local generators
Bravyi, S. B. (2010) · IEEE Information Theory Workshop (ITW) · doi:10.1109/cig.2010.5592872 · Cited by 4
Tailoring dynamical codes for biased noise: the X3Z3 Floquet code
Setiawan, F., & McLauchlan, C. (2025) · npj Quantum Information · doi:10.1038/s41534-025-01074-1 · Cited by 17
Quantum Computing, Cryptography and Compilers
Mosca, M. (2012) · IEEE International Symposium on Multiple-Valued Logic (ISMVL) · doi:10.1109/ismvl.2012.70 · Cited by 3
Reconfiguring quantum error-correcting codes for real-life errors
Ahsan, M., & Naqvi, S. A. Z. (2020) · Journal of Physics D Applied Physics · doi:10.1088/1361-6463/ab96eb · Cited by 3
Magic Mirror on the Wall, How to Benchmark Quantum Error Correction Codes, Overall?
Chatterjee, A., & Ghosh, S. (2024) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce60285.2024.00050 · Cited by 7
Feasibility of logical Bell state generation in memory assisted quantum networks
Galetsky, V., Vyas, N., Comin, A., & Nötzel, J. (2025) · Physical Review Research · doi:10.1103/rsrk-c7yg · Cited by 2
Fault tolerance against amplitude-damping noise using Bacon-Shor codes
My, L. D. H., Jayashankar, A., Mandayam, P., & Ng, H. K. (2025) · Physical Review Research · doi:10.1103/89td-45nl · Cited by 2
Zirak, A. (2023) · Quantum Information Processing · doi:10.1007/s11128-023-04155-2 · Cited by 2
Using Small Dimensional Quantum Error Correction Codes for High-Performance Quantum Communication
Jiao, D., Ashikhmin, A., Bayanifar, M., & Tirkkonen, O. (2023) · Globecom · doi:10.1109/globecom54140.2023.10436732 · Cited by 2
Encoding classical information in gauge subsystems of quantum codes
Nemec, A., & Klappenecker, A. (2022) · International Journal of Quantum Information · doi:10.1142/s0219749921500416 · Cited by 2
Quantum subsystem codes drived from negacyclic codes
Chen, J., Li, J., Lin, J., & Huang, Y. (2014) · International Computer Conference on Wavelet Active Media Technology and Information Processing (ICCWAMTIP) · doi:10.1109/iccwamtip.2014.7073373 · Cited by 2
Error Channels and the Threshold for Fault-tolerant Quantum ComputationPreprint
Eastin, B. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0710.2560 · Cited by 5
Characterizing Noise in Quantum Systems
Magesan, E. (2012) · UWSpace (University of Waterloo) · Cited by 4
Naus, H. W. L., & Versluis, R. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1811.09832 · Cited by 2
Neural Belief Propagation Decoders for Concatenated Calderbank-Shor-Steane Codes
Fan, J., & Zhang, J. (2024) · International Conference on Communications · doi:10.1109/icc51166.2024.10622478 · Cited by 1
Singkanipa, P., Xia, Z., & Lidar, D. A. (2025) · Quantum · doi:10.22331/q-2025-08-05-1821 · Cited by 2
Quantum Key Distribution in Multiparty Computation for Data Sorting by Entanglement
Sihare, S. R. (2025) · International Journal of Theoretical Physics · doi:10.1007/s10773-025-05944-4 · Cited by 1
Machine-learning-assisted pulse design for state preparation in a noisy environment
Wang, Z., Ma, H., Yan, Y., Wu, L.-A., & Wang, Z.-M. (2025) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2025.131081 · Cited by 1
Ouyang, Y., Jing, Y., & Brennen, G. K. (2025) · PRX Quantum · doi:10.1103/p28m-hb6x · Cited by 1
Multiqubit Rydberg Gates for Quantum Error Correction
Locher, D. F., Old, J., Brechtelsbauer, K., Holschbach, J., Büchler, H. P., Weber, S., & Müller, M. (2026) · PRX Quantum · doi:10.1103/j8fm-24cf · Cited by 1
Fault tolerance for holonomic quantum computation
Oreshkov, O., Brun, T. A., & Lidar, D. A. (2013) · Cambridge University Press eBooks · doi:10.1017/cbo9781139034807.019 · Cited by 1
Existence of Pauli-like stabilizers for every quantum error-correcting code
Kao, J.-Y., & Goan, H. (2023) · Physical Review A · doi:10.1103/physreva.108.032414 · Cited by 2
Effective Distance of Higher Dimensional HGPs and Weight-Reduced Quantum LDPC Codes
Tan, S. J. S., & Stambler, L. (2025) · Quantum · doi:10.22331/q-2025-10-28-1897 · Cited by 1
Efficient Decoding Scheme of Non-Uniform Concatenation Quantum Code with Deep Neural Network
Lin, C., Wang, Y., Wu, J., & Yang, G. (2021) · International Journal of Theoretical Physics · doi:10.1007/s10773-020-04706-8 · Cited by 1
On fixed-gap adiabatic quantum computationPreprint
Mizel, A. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1002.0846 · Cited by 1
Quantum Steganography and Quantum Error-CorrectionPreprint
Shaw, B. (2010) · arXiv (Cornell University) · doi:10.25549/usctheses-m3300 · Cited by 1
Practical Advances in Quantum Error Correction & Communication
Criger, D. B. (2013) · UWSpace (University of Waterloo) · Cited by 1
Decoding Algorithms for Hypergraph Subsystem Codes and Generalized Subsystem Surface CodesPreprint
Gayatri, V. V., & Sarvepalli, P. K. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1805.12542 · Cited by 1
Coherently Manipulated 2D Ion Crystal in a Monolithic Paul Trap
Wang, Y., Qiao, M., Cai, Z., Zhang, K., Jin, N., Wang, P., Chen, W., Luan, C., Du, B., Wang, H., et al. (2020) · Advanced Quantum Technologies · doi:10.1002/qute.202000068 · Cited by 18
Topological approach toward quantum codes with realistic physical constraintsPreprint
Yoshida, B. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1010.3282 · Cited by 1
Studying many-body physics through quantum coding theory
Yoshida, B. (2012) · DSpace@MIT (Massachusetts Institute of Technology)
Fault-tolerance in two-dimensional topological systems
Anderson, J. T. (2012) · UNM’s Digital Repository (University of New Mexico)
Accurate modeling of noise in quantum error correcting circuits
Arguedas, M. G. (2015) · SMARTech Repository (Georgia Institute of Technology)
Quantum recovery protocols for stabilizer codes: Deterministic Monte-Carlo simulation
Prousalis, K. P., Iliadis, A. A., & Konofaos, N. (2018) · AIP Advances · doi:10.1063/1.5024661
Lin, C., Yang, G., & Wu, J. (2020) · IEEE International Conference on Artificial Intelligence and Computer Applications (ICAICA) · doi:10.1109/icaica50127.2020.9182439
Applications of Locality and Asymmetry to Quantum Fault-Tolerance
Newman, M. (2018) · Deep Blue (University of Michigan)
(2011) · Elsevier eBooks · doi:10.1016/b978-0-12-383874-2.00009-6
New constructions of optimal subsystem codes
Wang, G., & Tang, C. (2022) · Computational and Applied Mathematics · doi:10.1007/s40314-022-02056-1
Quantum Teleportation: A Premier Quantum Communication Protocol
Im, C., Park, S., & Kim, J. (2024) · International Conference on Information and Communication Technology Convergence (ICTC) · doi:10.1109/ictc62082.2024.10827232
An Efficient Analytical Approach for Error Assessment in Quantum Circuits
Nikahd, E., Mohammadzadeh, N., & Shirmohammadi, Z. (2025) · IEEE Access · doi:10.1109/access.2025.3620026
Logical Operations with a Dynamical Qubit in Floquet-Bacon-Shor Code
Sun, X., Li, L., Guo, Z., Guo, Z., Huang, W., Huang, W., Liang, Y., Liang, Y., Liu, Y., Sun, D., et al. (2025) · Physical Review Letters · doi:10.1103/425n-6k9s · Cited by 3
Comparison of spin-qubit architectures for quantum error-correcting codes
Gutiérrez, M., Rojas-Arias, J. S., Obando, D., & Chang, C. Y. (2026) · Physical Review A · doi:10.1103/qlw3-xk2f · Cited by 3
Metadata
- 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 › 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
- Bacon-Shor code, quantum error correction, lower bounds, adversarial perturbations
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
