  We introduce harmonization, an ensembling method that combines several
"noisy" decoders to generate highly accurate decoding predictions. Harmonized
ensembles of MWPM-based decoders achieve lower logical error rates than their
individual counterparts on repetition and surface code benchmarks, approaching
maximum-likelihood accuracy at large ensemble sizes. We can use the degree of
consensus among the ensemble as a confidence measure for a layered decoding
scheme, in which a small ensemble flags high-risk cases to be checked by a
larger, more accurate ensemble. This layered scheme can realize the accuracy
improvements of large ensembles with a relatively small constant factor of
computational overhead. We conclude that harmonization provides a viable path
towards highly accurate real-time decoding.
