LEVERRIER, Anthony; ZÉMOR, Gilles

doi:10.1109/FOCS54457.2022.00117

Metadatos

Licencia de uso del documento

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

ZÉMOR, Gilles
Institut de Mathématiques de Bordeaux [IMB]
Cryptologie symétrique, cryptologie fondée sur les codes et information quantique [COSMIQ]

Idioma

Communication dans un congrès

Este ítem está publicado en

FOCS 2022 - IEEE 63rd Annual Symposium on Foundations of Computer Science, 2022-10-31, Denver. p. 872-883

IEEE

Resumen en inglés

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 theoremthat simultaneously gives a linearly growing minimum distance for the quantum code and recovers the local testability of the Dinur et al. code.< Leer menos

Palabras clave en inglés

Quantum error correcting code

Computer science

Codes

Quantum computing

Quantum mechanics

Parity check codes

Graph theory

URI

https://oskar-bordeaux.fr/handle/20.500.12278/190735

DOI

http://dx.doi.org/10.1109/FOCS54457.2022.00117

Proyecto ANR

From NISQ to LSQ: Bosonic and LDPC codes - ANR-22-PETQ-0006

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251