Protocols for Creating Anyons and Defects via Gauging

We address the problem of creating generic excitations in a given topological order and present a simple method for deriving anyon and defect ribbons. Our method relies on the notion of duality; by constructing a complete correspondence between two phases, we can use our knowledge of one to increase our knowledge of the other. In particular, gauging maps are known to relate topological orders to simpler theories; we leverage this fact to construct ribbon operators. We show how applying the (un)gauging map on a subdimensional region provides a way of creating anyons and symmetry defects on top of the ground state without destroying the underlying topological order. Aside from its conceptual value, our method provides a practical tool for quantum devices, as such gauging can be implemented using sequential unitary circuits or, in some cases, constant-depth adaptive circuits. We focus on using the Z3 toric code and quantum double of S3 as illustrative examples of our approach, constructing explicit circuits for excitations in these phases. The general applicability of our method is demonstrated by deriving unitary expressions for anyonic ribbon operators of various (twisted) quantum doubles.