  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.
