Canadian Summer School on Quantum Information (CSSQI) (10th : 2010)

Fast Decoders for Topological Quantum Codes Duclos-Cianci, Guillaume


Topological quantum computation and topological error correcting codes attracted a lot of interest recently because they require realistic nearest neighbors couplings and, by encoding the information in non-local topological degrees of freedom, they offer a very high resilience to local noise. I will 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 (Phys. Rev. Lett. 104, 050504 (2010)). 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 (16.5% vs 15.5%). I will introduce the intuitions behind the m! ethod and present new developments.

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