  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 approximations. 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.
