We study the decoding transition for quantum error correcting codes with the
help of a mapping to random-bond Wegner spin models.
Families of quantum low density parity-check (LDPC) codes with a finite
decoding threshold lead to both known models (e.g., random bond Ising and
random plaquette Z2 gauge models) as well as unexplored earlier generally
non-local disordered spin models with non-trivial phase diagrams. The decoding
transition corresponds to a transition from the ordered phase by proliferation
of extended defects which generalize the notion of domain walls to non-local
spin models. In recently discovered quantum LDPC code families with finite
rates the number of distinct classes of such extended defects is exponentially
large, corresponding to extensive ground state entropy of these codes.
Here, the transition can be driven by the entropy of the extended defects, a
mechanism distinct from that in the local spin models where the number of
defect types (domain walls) is always finite.Comment: 15 pages, 2 figure