Efficient decoding of random errors for quantum expander codes

Omar Fawzi (1) , Antoine Grospellier (2) , Anthony Leverrier (2)

1 LIP - Laboratoire de l'Informatique du Parallélisme
2 SECRET - Security, Cryptology and Transmissions

We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of Leverrier, Tillich and Zémor can correct a constant fraction of random errors with very high probability. This is the first construction of a constant-rate quantum LDPC code with an efficient decoding algorithm that can correct a linear number of random errors with a negligible failure probability. Finding codes with these properties is also motivated by Gottesman's construction of fault tolerant schemes with constant space overhead.

Domaines: Physique Quantique [quant-ph]; Théorie de l'information et codage [math.IT]

Omar Fawzi, Antoine Grospellier, Anthony Leverrier. Efficient decoding of random errors for quantum expander codes. 8th colloquium of the GDR IQFA - Ingénierie Quantique, des Aspects Fondamentaux aux Applications, Nov 2017, Nice, France. ⟨hal-01671496⟩