Fast decoders for topological quantum codes.
We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the quantum information stored in the ground space of a topologically ordered system and to decode topological error-correcting codes. For a system of linear size l, our algorithm runs in time logl compared to l{6} needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold.
Duclos-Cianci
Guillaume
G
Département de Physique, Université de Sherbrooke, Québec, Canada.
Poulin
David
D