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Topological quantum error-correcting codes are defined by geometrically localchecks on a two-dimensional lattice of quantum bits (qubits), making themparticularly well suited for fault-tolerant quantum information processing.Here, we present a decoding algorithm for topological codes that is faster thanpreviously known algorithms and applies to a wider class of topological codes.Our algorithm makes use of two methods inspired from statistical physics:renormalization groups and mean-field approximations. First, the topologicalcode is approximated by a concatenated block code that can be efficientlydecoded. To improve this approximation, additional consistency conditions areimposed between the blocks, and are solved by a belief propagation algorithm.

A renormalization group decoding algorithm for topological quantum codes