Higher order topological superconductors as generators of quantum codes

Understand

We show that interactions can drive a class of higher order topological superconductors (HOTSC) into symmetry enriched topologically ordered phases exemplified by topological quantum error correcting codes.

• In two dimensions, interacting HOTSC realize various topologically ordered surface and color codes.
• In three dimensions, interactions can drive HOTSC protected by subsystem symmetries into recently discovered fracton phases.
• We explicitly relate fermion parity operators underlying the gapless excitations of the HOTSC to the Wilson algebra of symmetry enriched quantum codes.