Performance enhancement of surface codes via recursive minimum-weight perfect-match decoding

The minimum weight perfect matching (MWPM) decoder is the standard decoding strategy for quantum surface codes. However, it suffers a harsh decrease in performance when subjected to biased or nonidentical quantum noise. In this work, we modify the conventional MWPM decoder so that it considers the biases, the nonuniformities, and the relationship between X, Y, and Z errors of the constituent qubits of a given surface code. Our modified approach, which we refer to as the recursive MWPM decoder, obtains an 18% improvement in the probability threshold p(th) under depolarizing noise. We also obtain significant performance improvements when considering biased noise and independent nonidentically distributed (i.ni.d.) error models derived from measurements performed on state-of-the-art quantum processors. In fact, when subjected to i.ni.d. noise, the recursive MWPM decoder yields a performance improvement of 105.5% over the conventional MWPM strategy, and in some cases, it even surpasses the performance obtained over the well-known depolarizing channel.