A renormalization group decoding algorithm for topological quantum codes

Details A renormalization group decoding algorithm for topological quantum codes A renormalization group decoding algorithm for topological quantum codes

2010-06-07

arxiv.org/abs/1006.1362v1

Information Theory Workshop (ITW), 2010 IEEE , pp.1-5, Aug. 30 2010-Sept. 3 2010

Physics

Quantum Physics

Scientific paper

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.

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