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 non-identical quantum noise. In this work, we modify the conventional MWPM decoder so that it considers the biases, the non-uniformities 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 non-identically 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.