Pauli topological subsystem codes from Abelian anyon theories

Understand

We construct Pauli topological subsystem codes characterized by arbitrary two-dimensional Abelian anyon theories--this includes anyon theories with degenerate braiding relations and those without a gapped boundary to the vacuum.

• Our work both extends the classification of two-dimensional Pauli topological subsystem codes to systems of composite-dimensional qudits and establishes that the classification is at least as rich as that of Abelian anyon theories.
• We exemplify the construction with topological subsystem codes defined on four-dimensional qudits based on the $\mathbb{Z}_4^{(1)}$ anyon theory with degenerate braiding relations and the chiral semion theory--both of which cannot be captured by topological stabilizer codes.
• The construction proceeds by "gauging out" certain anyon types of a topological stabilizer code.