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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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“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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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 8
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 11
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
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