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Communication Dans Un Congrès Année : 2022

Quantum Tanner codes

Résumé

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 c3 locally testable code by Dinur et al. 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 al. 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 al. code.
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Dates et versions

hal-03926730 , version 1 (06-01-2023)

Identifiants

Citer

Anthony Leverrier, Gilles Zémor. Quantum Tanner codes. FOCS 2022 - IEEE 63rd Annual Symposium on Foundations of Computer Science, Oct 2022, Denver, United States. pp.872-883, ⟨10.1109/FOCS54457.2022.00117⟩. ⟨hal-03926730⟩
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