Topological quantum error-correcting codes are defined by geometrically local checks on a two-dimensional lattice of quantum bits (qubits), making them particularly well suited for fault-tolerant quantum information processing. Here, we present a decoding algorithm for topological codes that is faster than previously 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

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... pproximations. First, the topological code is approximated by a concatenated block code that can be efficiently decoded. To improve this approximation, additional consistency conditions are imposed between the blocks, and are solved by a belief propagation algorithm.