Protocols for Creating Anyons and Defects via Gauging

Abstract

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 work, 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.

7+18 pages, 3+8 figures. v2: added various references + minor text revisions. v3: additional text revisions for clarity + correction of minor errors in the supplementary

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• Universal fault tolerant quantum computation in 2D without getting tied in knots