  flip is an extremely simple and maximally local classical decoder which has
been used to great effect in certain classes of classical codes. When applied
to quantum codes there exist constant-weight errors (such as half of a
stabiliser) which are uncorrectable for this decoder, so previous studies have
considered modified versions of flip, sometimes in conjunction with other
decoders. We argue that this may not always be necessary, and present numerical
evidence for the existence of a threshold for flip when applied to the looplike
syndromes of a three-dimensional toric code on a cubic lattice. This result can
be attributed to the fact that the lowest-weight uncorrectable errors for this
decoder are closer (in terms of Hamming distance) to correctable errors than to
other uncorrectable errors, and so they are likely to become correctable in
future code cycles after transformation by additional noise. Introducing
randomness into the decoder can allow it to correct these "uncorrectable"
errors with finite probability, and for a decoding strategy that uses a
combination of belief propagation and probabilistic flip we observe a threshold
of $\sim5.5\%$ under phenomenological noise. This is comparable to the best
known threshold for this code ($\sim7.1\%$) which was achieved using belief
propagation and ordered statistics decoding [Higgott and Breuckmann, 2022], a
strategy with a runtime of $O(n^3)$ as opposed to the $O(n)$ ($O(1)$ when
parallelised) runtime of our local decoder. We expect that this strategy could
be generalised to work well in other low-density parity check codes, and hope
that these results will prompt investigation of other previously overlooked
decoders.
