Gauge Theories and Stabilizer Codes: From Abelian to non-Abelian models

We summarize several different gauge-theory-related formulations of quantum stabilizer codes on a lattice. Examples include the toric code and the X-cube model. The latter carries fractonic excitations. We compare and contrast these formulations, and investigate their generalizations to non-Abelian gauge theories. In particular, we construct the non-Abelian anyon model from gauging the SWAP symmetry of double-layer Z₂ gauge theory with matter and compare it with the D₄ quantum double model.