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We introduce harmonization, an ensembling method that combines several"noisy" decoders to generate highly accurate decoding predictions. Harmonizedensembles of MWPM-based decoders achieve lower logical error rates than theirindividual counterparts on repetition and surface code benchmarks, approachingmaximum-likelihood accuracy at large ensemble sizes. We can use the degree ofconsensus among the ensemble as a confidence measure for a layered decodingscheme, in which a small ensemble flags high-risk cases to be checked by alarger, more accurate ensemble. This layered scheme can realize the accuracyimprovements of large ensembles with a relatively small constant factor ofcomputational overhead. We conclude that harmonization provides a viable pathtowards highly accurate real-time decoding.

Efficient near-optimal decoding of the surface code through ensembling