Appears in collection : 2017 - T3 - WS3 - Quantum information theory

We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of [1] 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 alinear 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. Joint work with Antoine Grospellier and Omar Fawzi[1] https://arxiv. org/abs/1504. 00822