Decoder construction for higher-dimensional translation-invariant codes

Determine whether the structure theorem for higher-dimensional translation-invariant quantum codes can be applied to construct decoders for higher-dimensional translation-invariant codes, following the matching-decoder approaches cited by the authors.

Background

The paper reduces the considered higher-dimensional translation-invariant codes to stacks of D-dimensional toric codes under Hamiltonian equivalence. It remains unresolved whether this structural reduction can be used constructively to develop decoders for higher-dimensional translation-invariant codes, analogous to the matching-decoder methods referenced in the discussion.