Creating and manipulating anyons and symmetry defects in topological phases, especially those with a non-Abelian character, constitutes a primitive for topological quantum computation. We provide a physical protocol for implementing the ribbon operators of non-Abelian anyons and symmetry defects. We utilize dualities, in particular, the Kramers-Wannier or gauging map, which have previously been used to construct topologically ordered ground states by relating them to simpler states. In this Letter, ribbon operators are implemented by applying a gauging procedure to a lower-dimensional region of such states. This protocol uses sequential unitary circuits or, in certain cases, constant-depth adaptive circuits. We showcase this for anyons and defects in the ${\mathbb{Z}}_3$ toric code and $S_3$ quantum double. The general applicability of our method is demonstrated by deriving unitary expressions for ribbon operators of various (twisted) quantum doubles.

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• Anyons
• Quantum circuits
• Topological phases of matter
• Topological quantum computing
• Discrete symmetries in condensed matter
• Duality
• Gauge symmetries
• Spin lattice models