Fast Decoders for Topological Quantum Codes

Details Fast Decoders for Topological Quantum Codes Fast Decoders for Topological Quantum Codes

2009-11-03

arxiv.org/abs/0911.0581v2

Phys. Rev. Lett. 104 050504 (2010)

Physics

Quantum Physics

4 pages, 4 figures

Scientific paper

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 log L compared to L^6 needed for the minimum-weight perfect matching algorithm previously used in this context and achieves a higher depolarizing error threshold.

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