The DOI matches its Crossref record; 28 of the 29 references it cites were found in a registry or an index.
Quantum Tanner codes
Open accessAbstract
Tanner codes are long error correcting codes obtained from short codes and a graph, with bits on the edges and parity-check constraints from the short codes enforced at the vertices of the graph. Combining good short codes together with a spectral expander graph yields the celebrated expander codes of Sipser and Spielman, which are asymptotically good classical LDPC codes. In this work we apply this prescription to the left-right Cayley complex that lies at the heart of the recent construction of a c3locally testable code by Dinur et at. Specifically, we view this complex as two graphs that share the same set of edges. By defining a Tanner code on each of those graphs we obtain two classical codes that together define a quantum code. This construction can be seen as a simplified variant of the Panteleev and Kalachev asymptotically good quantum LDPC code, with improved estimates for its minimum distance. This quantum code is closely related to the Dinur et at. code in more than one sense: indeed, we prove a theorem that simultaneously gives a linearly growing minimum distance for the quantum code and recovers the local testability of the Dinur et at. code.
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?
The cited source says what the claim attributes to it.
In the citing paper
“The latter were shown39,40 to be asymptotically ‘good’ in the sense of offering a constant encoding rate and linear distance: a parameter quantifying the number of correctable errors.”
From High-threshold and low-overhead fault-tolerant quantum memory (2024) · cites this paper as [40]
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
Low-density parity-check codes
Gallager, R. G. (1962) · IEEE Transactions on Information Theory · doi:10.1109/tit.1962.1057683 · Cited by 10,727
Fault-tolerant quantum computation by anyons
Kitaev, A. Y. (2003) · Annals of Physics · doi:10.1016/s0003-4916(02)00018-0 · Cited by 7,238
A recursive approach to low complexity codes
Tanner, R. M. (1981) · IEEE Transactions on Information Theory · doi:10.1109/tit.1981.1056404 · Cited by 3,176
Error Correcting Codes in Quantum Theory
Steane, A. M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.793 · Cited by 2,677
Good 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
Expander graphs and their applications
Hoory, S., Linial, N., & Wigderson, A. (2006) · Bulletin of the American Mathematical Society · doi:10.1090/s0273-0979-06-01126-8 · Cited by 1,679
Sipser, M., & Spielman, D. A. (1996) · IEEE Transactions on Information Theory · doi:10.1109/18.556667 · Cited by 945
Checking computations in polylogarithmic time
Babai, L., Fortnow, L., Levin, L. A., & Szegedy, M. (1991) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/103418.103428 · Cited by 627
Tillich, J., & Zémor, G. (2014) · IEEE Transactions on Information Theory · doi:10.1109/tit.2013.2292061 · Cited by 418
Quantum Low-Density Parity-Check Codes
Breuckmann, N. P., & Eberhardt, J. N. (2021) · PRX Quantum · doi:10.1103/prxquantum.2.040101 · Cited by 328
Research works printed but not linked: 2
- Lin, 2022, c3-local testable codes from lossless expanders, arXiv preprint arXiv:2201.11369 · arXiv
- Gottesman, 1997, Stabilizer codes and quantum error correction
Cited by
Sorted by citations
Items 101–136 of 136
Quantum LDPC Codes From Intersecting Subsets
Ostrev, D. (2024) · IEEE Transactions on Information Theory · doi:10.1109/tit.2024.3402091 · Cited by 3
First, U. A., & Kaufman, T. (2024) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3618260.3649625 · Cited by 1
How Random CSPs Fool Hierarchies
Chan, S. O., Ng, H. T., & Peng, S. (2024) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3618260.3649613 · Cited by 1
Decoding Quasi-Cyclic Quantum LDPC Codes
Golowich, L., & Guruswami, V. (2024) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs61266.2024.00029 · Cited by 1
Dai, S., & Li, R. (2025) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3717823.3718113 · Cited by 8
On the Computational Power of QAC0 with Barely Superlinear Ancillae
Anshu, A., Dong, Y., Ou, F., & Yao, P. (2025) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3717823.3718189 · Cited by 1
Targeted Clifford logical gates for hypergraph product codes
Patra, A., & Barg, A. (2025) · Quantum · doi:10.22331/q-2025-08-29-1842 · Cited by 5
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
Trapped Ion Quantum Repeaters with Entanglement Distillation based on Quantum LDPC Codes
Kang, A., Guha, S., Rengaswamy, N., & Seshadreesan, K. P. (2023) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce57702.2023.00131 · Cited by 2
From Grassmannian to Simplicial High-Dimensional Expanders
Golowich, L. (2023) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs57990.2023.00099 · Cited by 1
Partitioning qubits in hypergraph product codes to implement logical gatesPreprint
Quintavalle, A. O., Webster, P., & Vasmer, M. (2022) · arXiv (Cornell University) · doi:10.17169/refubium-41189 · Cited by 1
On robust testability of product of random codes
Kalachev, G. V., & Panteleev, P. (2022) · Academician O.B. Lupanov International Scientific Seminar "Discrete Mathematics and Its Applications" · doi:10.20948/dms-2022-84
Asymptotically good families of quantum and locally testable classical LDPC codes
Kalachev, G. V., & Panteleev, P. (2023) · Mathematical Problems of Cybernetics · doi:10.20948/mvk-2023-111
Quaternary-Binary Message-Passing Decoder for Quantum LDPC Codes
Chytas, D., Raveendran, N., Pradhan, A. K., & Vasic, B. V. (2023) · Globecom · doi:10.1109/globecom54140.2023.10436874
Increasing the distance of topological codes with time vortex defects
Kishony, G., & Berg, E. (2026) · Quantum · doi:10.22331/q-2026-02-23-2006
A new explicit construction of unique-neighbor expanders
Zhu, W. (2025) · JUSTC · doi:10.52396/justc-2023-0165
Color Code with a Logical Control- S Gate Using Transversal T Rotations
Brown, B. J. (2025) · Physical Review Letters · doi:10.1103/lwxd-fdlb · Cited by 3
Advancing Finite-Length Quantum Error Correction Using Generalized Bicycle Codes
Mostad, O. Å., Lin, H.-Y., Rosnes, E., Lee, D.-S., & Lai, C. (2025) · International Symposium on Turbo Codes and Iterative Information Processing · doi:10.1109/istc65386.2025.11154497
Mean Estimation in High-Dimensional Binary Timeinhomogeneous Markov Gaussian Mixture Models
Kadry, A. E. L., Zhang, Y., & Weinberger, N. (2025) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit63088.2025.11195426
Moveless: Minimizing QEC Overhead on QCCDS via Versatile Execution and Low Excess Shuttling
Khan, S., Vittal, S., Brown, K. R., & Baker, J. (2025) · IEEE International Conference on Quantum Computing and Engineering (QCE) · doi:10.1109/qce65121.2025.00075 · Cited by 1
Almost optimal geometrically local quantum LDPC codes in any dimension
Li, X., Lin, T.-C., Wills, A., & Hsieh, M.-H. (2026) · Nature Communications · doi:10.1038/s41467-026-69031-w
Fault-Tolerant Quantum Input/Output
Christandl, M., Fawzi, O., & Goswami, A. (2026) · IEEE Transactions on Information Theory · doi:10.1109/tit.2026.3672442 · Cited by 9
Decoding correlated errors in quantum LDPC codes
Maan, A. S., García-Herrero, F., Paler, A., & Savin, V. (2026) · Nature Communications · doi:10.1038/s41467-026-70556-3
Quantum key distribution and quantum error correction with bosonic systems
Denys, A. (2024) · theses.fr (ABES) · doi:10.70675/c51a18fbz5b6fz4912zb5a1z470c35920675
Noisy Soft Syndrome Decoding of Quantum LDPC Codes for the Quantum Erasure Channel
Gayathri, R., Bhatnagar, S., & Kumar, P. V. (2026) · National Conference on Communications · doi:10.1109/ncc68160.2026.11478883
High Rate Efficient Local List Decoding from HDX
Dikstein, Y., Hopkins, M., Pitassi, T., & Impagliazzo, R. (2026) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3798129.3800886
Partial Self-Correction in Layer Codes
Williamson, D. J. (2026) · Physical Review Letters · doi:10.1103/mb89-8436 · Cited by 7
Optimal, Best-Known Divisible Binary Codes and Related Quantum Codes
Chen, H., Yu, C., Chen, Y., Xie, C., Sun, Z., & Zhu, S. (2026) · IEEE Transactions on Information Theory · doi:10.1109/tit.2026.3719641
A Streaming Architecture for Quantum Error Syndrome Compression at 4 Kelvin
Papanikolaou, P., Hou, R., Volk, J. E., & Tzimpragos, G. (2026) · Proceedings - International Symposium on Computer Architecture/Proceedings · doi:10.1109/isca66397.2026.00071
On the Analysis of Stopping Sets Associated with the Quantum Hypergraph Product Code
Prabhu, J. S., Gayathri, R., & Kumar, P. V. (2026) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit62367.2026.11654127
ADMM Decoding of Quantum LDPC Codes
Lyu, J., & He, G. (2026) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit62367.2026.11653953
Quantum Locally Recoverable Codes With Intersecting Recovery Sets
Bu, K., Gu, W., & Li, X. (2026) · IEEE Transactions on Information Theory · doi:10.1109/tit.2026.3732133 · Cited by 9
General construction of quantum error-correcting codes from multiple classical codes
Anonymous, Li, M.-Y., Li, C., & Zhai, H. (2026) · Physical review. B./Physical review. B · doi:10.1103/6c3l-8n19
Pêlαγos: An Adaptive GPU Decoder for Error Correction Simulations of Quantum LDPC Codes
Diamantopoulos, D., von Niederhäusern, L., Anghel, A. S., Pletka, R. A., Kayi, A., Müller, T., Papandreou, N., Blanuša, J., Sarafijanović, S., Gonzalez, N. M., et al. (2026) · IEEE International Conference on Quantum Software (QSW) · doi:10.1109/qsw72780.2026.00025
Quantum Error Correction Survey
Mahmud, M.-E.-H., Jain, R. K., Yang, Z., Tian, C., Kompella, R. R., Nejabati, R., Kaur, E., Erbad, A., & Abdallah, M. M. (2026) · IEEE Access · doi:10.1109/access.2026.3737721
Complete classification of weight-3 logical operators in the Face Centered Cubic lattice CSS code
Kulkarni, R. (2026) · Discover Quantum Science · doi:10.1007/s44464-026-00047-3
Metadata
- Authors
- Leverrier, A., & Zemor, G.
- Affiliations
- Institut national de recherche en sciences et technologies du numérique (FR)
- Institut de Mathématiques de Bordeaux,Bordeaux,France,UMR 5251
- ORCID
- Leverrier, Anthony
- Venue
- 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)
- Publisher
- IEEE
- Published
- 2022-10
- Pages
- 872-883
- ISSN
- 0272-5428 (ISSN-L)
- OpenAlex
- W4226180919
- Cited by
- 140
- References
- 29
- Citations by year
- 2026: 25 · 2025: 48 · 2024: 40 · 2023: 21 · 2022: 6
- FWCI
- 15.86
- Type
- conference paper
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Annual Symposium on Foundations of Computer Science (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- HAL (submittedVersion, other-oa)
- HAL (submittedVersion, cc-by)
- Oskar-Bordeaux (Universite de Bordeaux) (submittedVersion)
- arXiv (Cornell University) (cc-by)
- Funders
- Agence Nationale de la Recherche
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Coding theory and cryptography
- Physical Sciences › Computer Science › Computer Networks and Communications › Error Correcting Code Techniques
- Keywords
- quantum LDPC codes, expander codes, locally testable codes, minimum distance, 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
