Asymptotically good Quantum and locally testable classical LDPC codes
Abstract
We study classical and quantum LDPC codes of constant rate obtained by the lifted product construction over non-abelian groups. We show that the obtained families of quantum LDPC codes are asymptotically good, which proves the qLDPC conjecture. Moreover, we show that the produced classical LDPC codes are also asymptotically good and locally testable with constant query and soundness parameters, which proves a well-known conjecture in the field of locally testable codes.
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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 [39]
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References 67 · Cited by 222
- Authors
- Panteleev, P., & Kalachev, G.
- Affiliations
- Lomonosov Moscow State University (RU)
- Venue
- Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing
- Publisher
- ACM
- Published
- 2022-06-09
- Pages
- 375-388
- OpenAlex
- W3213933684
- Cited by
- 222
- References
- 67
- Citations by year
- 2026: 42 · 2025: 67 · 2024: 60 · 2023: 33 · 2022: 18 · 2021: 1 · 2017: 1
- FWCI
- 24.61
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- ACM Symposium on Theory of Computing (STOC) (publishedVersion)
- 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, asymptotically good codes, non-abelian groups, locally testable codes
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