Protocols for Creating Anyons and Defects via Gauging

• URL: http://arxiv.org/abs/2411.04181v1
• Date: Wed, 06 Nov 2024 19:00:01 GMT
• Title: Protocols for Creating Anyons and Defects via Gauging
• Authors: Anasuya Lyons, Chiu Fan Bowen Lo, Nathanan Tantivasadakarn, Ashvin Vishwanath, Ruben Verresen,
• Abstract summary: We provide a physical protocol for implementing the ribbon operators of non-Abelian anyons and symmetry defects. We showcase this for anyons and defects in the $mathbbZ_3$ toric code and $S_3$ quantum double.
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• 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.

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