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Fast Decoders for Topological Quantum Codes
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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.
Forward citations
Cited by 2 Pith papers
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Kinetics of sliding-window quantum error correction
Sliding-window decoding of topological quantum codes is effectively described by a parity-conserving reaction-diffusion process in which the decoding rate 1/W acts as a relevant perturbation, yielding exponential memo...
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Under three stated assumptions, a resource-free static surface-code patch cannot sharply measure the magic axis at polynomial acceptance; it must pay with a resource, leave the dilute regime, or accept exponentially rarely.
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