Generalized Belief Propagation Algorithms for Decoding of Surface Codes

Belief propagation (BP) is well-known as a low complexity decoding algorithm with strong performance for important classes of quantum error correcting codes, e.g. notably the low-density parity check (LDPC) code class random expander codes. However, it also that BP breaks down when facing topological codes such surface code, where naive fails entirely to reach below-threshold regime, i.e. regime correction becomes useful. Previous works have shown, this can be remedied by resorting post-processing decoders outside framework BP. In work, we present generalized belief method an outer re-initialization loop successfully decodes opposed recovers sub-threshold known from tailored and statistical-mechanical mappings. We report threshold 17% under independent bit-and phase-flip data noise (to compared ideal 20.6%) value 14%$under depolarizing (compared 18.9%), which are on par thresholds achieved non-BP methods.