Protocols for Creating Anyons and Defects via Gauging

TL;DR

This paper presents a physical protocol using gauging dualities to create and manipulate non-Abelian anyons and symmetry defects in topological phases, facilitating advances in topological quantum computation.

Contribution

It introduces a novel method to implement ribbon operators for non-Abelian anyons and defects via gauging procedures applied to lower-dimensional regions.

Findings

Demonstrated protocol for $ ext{Z}_3$ toric code and $S_3$ quantum double

Derived unitary expressions for ribbon operators of various quantum doubles

Applicable to a broad class of topological phases and defects

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.