Constructions and performance of classes of quantum LDPC codes
  Two methods for constructing quantum LDPC codes are presented. We explain how to overcome the difficulty of finding a set of low weight generators for the stabilizer group of the code. Both approaches are based on some graph representation of the generators of the stabilizer group and on simple local rules that ensure commutativity. A message passing algorithm for generic quantum LDPC codes is also introduced. Finally, we provide two specific examples of quantum LDPC codes of rate 1/2 obtained by our methods, together with a numerical simulation of their performance over the depolarizing channel. 
T. Camara, H. Ollivier and J.-P. Tillich