Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength

Jean-Pierre Tillich (1) , Gilles Zémor (2)

1 SECRET - Security, Cryptology and Transmissions
2 IMB - Institut de Mathématiques de Bordeaux

The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with fixed non-zero rate is logarithmic in the blocklength. We propose a construction of quantum LDPC codes with fixed non-zero rate and prove that the minimum distance grows proportionally to the square root of the blocklength.

Mots clés: CSS codes; LDPC codes; quantum codes

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

Jean-Pierre Tillich, Gilles Zémor. Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength. IEEE Transactions on Information Theory, 2014, 60 (2), pp.1193-1202. ⟨10.1109/TIT.2013.2292061⟩. ⟨hal-00931764⟩