  Fracton topological phases have a large number of materialized symmetries
that enforce a rigid structure on their excitations. Remarkably, we find that
the symmetries of a quantum error-correcting code based on a fracton phase
enable us to design decoding algorithms. Here we propose and implement decoding
algorithms for the three-dimensional X-cube model. In our example, decoding is
parallelized into a series of two-dimensional matching problems, thus
significantly simplifying the most time consuming component of the decoder. We
also find that the rigid structure of its point excitations enable us to obtain
high threshold error rates. Our decoding algorithms bring to light some key
ideas that we expect to be useful in the design of decoders for general
topological stabilizer codes. Moreover, the notion of parallelization unifies
several concepts in quantum error correction. We conclude by discussing the
broad applicability of our methods, and we explain the connection between
parallelizable codes and other methods of quantum error correction. In
particular we propose that the new concept represents a generalization of
single-shot error correction.
