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.
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Quantum Tanner codes were shown to be asymptotically 'good' in the sense of offering a constant encoding rate and linear distance.
“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]
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Freire, B. C. A., Delfosse, N., & Leverrier, A. (2025) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit63088.2025.11195424 · Cited by 4 · see citing works
Self-citationFault-Tolerant Quantum Computation with Constant Overhead for General Noise
Christandl, M., Fawzi, O., & Goswami, A. (2025) · PRX Quantum · doi:10.1103/k4cm-pp9p · Cited by 2 · see citing works
An Improved Decimation Technique for Erasure Decoding of Quantum LDPC Codes
Gayathri, R., Bhatnagar, S., Vaishya, A., & Kumar, P. V. (2025) · IEEE Information Theory Workshop (ITW) · doi:10.1109/itw62417.2025.11240302 · Cited by 2 · see citing works
Opportunities in full-stack design of low-overhead fault-tolerant quantum computation
Zhou, H., Cain, M., & Lukin, M. D. (2025) · Nature Computational Science · doi:10.1038/s43588-025-00895-6 · Cited by 2 · see citing works
Quantum Maxwell Erasure Decoder for qLDPC codes
Freire, B. C. A., Régent, F.-M. L., & Leverrier, A. (2026) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit62367.2026.11654048 · Cited by 2 · see citing works
Self-citationCharacterizing the Burst Error Correction Ability of Quantum Cyclic Codes
Fan, J., & Hsieh, M.-H. (2026) · IEEE Transactions on Information Theory · doi:10.1109/tit.2026.3659999 · Cited by 2 · see citing works
Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes
Gu, S., & Soleimanifar, M. (2026) · IEEE Transactions on Information Theory · doi:10.1109/tit.2026.3715538 · Cited by 1 · see citing works
Pacenti, M., & Vasic, B. V. (2024) · Allerton Conference on Communication, Control, and Computing · doi:10.1109/allerton63246.2024.10735283 · Cited by 2 · see citing works
Local testability of distance-balanced quantum codes
Wills, A., Lin, T.-C., & Hsieh, M.-H. (2024) · npj Quantum Information · doi:10.1038/s41534-024-00908-8 · Cited by 2 · see citing works
Energy Barrier of Hypergraph Product Codes
Zhao, G., Doherty, A. C., & Kim, I. H. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.180601 · Cited by 2 · see citing works
Asymptotically Good CSS-T Codes and a New Construction of Triorthogonal Codes
Berardini, E., Dastbasteh, R., Martínez, J. E., Jain, S., & Larrarte, O. S. (2025) · IEEE Journal on Selected Areas in Information Theory · doi:10.1109/jsait.2025.3582156 · Cited by 2 · see citing works
On the Efficacy of the Peeling Decoder for the Quantum Expander Code
Prabhu, J. S., Vaishya, A., Bhatnagar, S., Kolhe, A. M., Lalitha, V., & Kumar, P. V. (2025) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit63088.2025.11195550 · Cited by 1 · see citing works
QBEL: Quantum Burst Error Locating Codes
Con, R., Gabrys, R., & Yaakobi, E. (2025) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit63088.2025.11195453 · Cited by 1 · see citing works
Turbo-XZ Algorithm: Low-Latency Decoders for Quantum LDPC Codes
Raveendran, N., Boutillon, E., & Vasic, B. V. (2023) · International Symposium on Turbo Codes and Iterative Information Processing · doi:10.1109/istc57237.2023.10273490 · Cited by 2 · see citing works
List Decoding of Tanner and Expander Amplified Codes from Distance Certificates
Jeronimo, F. G., Srivastava, S., & Tulsiani, M. (2023) · Annual Symposium on Foundations of Computer Science · doi:10.1109/focs57990.2023.00102 · Cited by 2 · see citing works
Explicit Two-Sided Unique-Neighbor Expanders
Hsieh, J.-T., McKenzie, T., Mohanty, S., & Paredes, P. (2024) · ACM Symposium on Theory of Computing (STOC) · doi:10.1145/3618260.3649705 · Cited by 2 · see citing works
Baspin, N., & Williamson, D. J. (2026) · Quantum · doi:10.22331/q-2026-04-24-2083 · Cited by 1 · see citing works
Collective Bit Flipping-Based Decoding of Quantum LDPC Codes
Chytas, D., Raveendran, N., & Vasic, B. V. (2025) · IEEE Transactions on Communications · doi:10.1109/tcomm.2025.3535897 · Cited by 1 · see citing works
Asymptotically Good Generalized Quantum Tanner Codes
Mostad, O. Å., Rosnes, E., & Lin, H.-Y. (2025) · IEEE Journal on Selected Areas in Information Theory · doi:10.1109/jsait.2025.3594310 · Cited by 1 · see citing works
Enhanced Min-Sum Decoding of Quantum Codes with Iteration Dynamics Memory
Chytas, D., Raveendran, N., & Vasic, B. V. (2025) · IEEE International Symposium on Information Theory (ISIT) · doi:10.1109/isit63088.2025.11195509 · Cited by 1 · see citing works
A Variant of the Bravyi–Terhal Bound for Arbitrary Boundary Conditions
Arnault, F., Gaborit, P., Rozendaal, W., Saussay, N., & Zémor, G. (2025) · IEEE Transactions on Information Theory · doi:10.1109/tit.2025.3629670 · Cited by 1 · see citing works
Toward Self-Correcting Quantum Codes for Neutral Atom Arrays
Guo, J., Hong, Y., Kaufman, A. M., & Lucas, A. (2025) · PRX Quantum · doi:10.1103/mfmt-fwkg · Cited by 1 · see citing works
Approximate Quantum Error Correction with 1D Log-Depth Circuits
Liu, G., Du, Z., Liu, Z.-W., & Ma, X. (2026) · PRX Quantum · doi:10.1103/7rzk-2jyh · Cited by 1 · see citing works
QUITS: A modular Qldpc code circUIT Simulator
Kang, M., Lin, Y., Yao, H., Gökduman, M., Meinking, A., & Brown, K. R. (2025) · Quantum · doi:10.22331/q-2025-12-05-1931 · Cited by 3 · see citing works
- 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 › Computer Science › Artificial Intelligence › 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
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