Generalized Belief Propagation Algorithms for Decoding of Surface Codes

Generalized Belief Propagation Algorithms for Decoding of Surface Codes

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Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g.notably for the quantum low-density parity check (LDPC) code class of random expander codes.However, it is also well-known that the performance of BP breaks down when facing topological codes such as the surface code, where naive BP jeff rosenstock buffalo fails entirely to reach a below-threshold regime, i.

e.the regime where error correction becomes useful.Previous works have shown, that this can be remedied by resorting to post-processing decoders outside the framework of BP.In this work, we present a generalized belief propagation method with an outer re-initialization loop that successfully decodes surface codes, i.

e.opposed to naive BP it recovers the sub-threshold regime known from decoders tailored to the surface code and from statistical-mechanical mappings.We report a threshold of $ extit{17%}$ under independent bit-and phase-flip data noise (to be compared to the ideal threshold of $ extit{20.6%}$) and a threshold value of $ extit{14%}$ under depolarizing data noise (compared to the ideal threshold of $ extit{18.

9%}$), which are whole wheat phyllo dough on par with thresholds achieved by non-BP post-processing methods.