LEVERRIER, Anthony; ZÉMOR, Gilles

doi:10.1109/TIT.2023.3267945

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LEVERRIER, Anthony
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]

ZÉMOR, Gilles
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

IEEE Transactions on Information Theory. 2022-12-09, vol. 69, n° 8, p. 5100-5115

Institute of Electrical and Electronics Engineers

Résumé en anglais

We introduce sequential and parallel decoders for quantum Tanner codes. When the Tanner code construction is applied to a sufficiently expanding square complex with robust local codes, we obtain a family of asymptotically good quantum lowdensity parity-check codes. In this case, our decoders provably correct arbitrary errors of weight linear in the code length, respectively in linear or logarithmic time. The same decoders are easily adapted to the expander lifted product codes of Panteleev and Kalachev. Along the way, we exploit recently established bounds on the robustness of random tensor codes to give a tighter bound on the minimum distance of quantum Tanner codes.< Réduire

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190406

DOI

http://dx.doi.org/10.1109/TIT.2023.3267945

Project ANR

From NISQ to LSQ: Bosonic and LDPC codes - ANR-22-PETQ-0006
Algorithmes quantiques pour données massives - ANR-18-CE47-0010

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251