Topological Order with a Twist: Ising Anyons from an Abelian Model

TL;DR

This paper demonstrates how topological defects in the toric code can emulate Ising anyons, revealing new ways to realize non-Abelian anyons in Abelian models for topological quantum computing.

Contribution

It shows that braiding and fusing defects in the toric code produce outcomes equivalent to Ising anyons, introducing a novel method to realize non-Abelian anyons.

Findings

Defects in the toric code can emulate Ising anyons.

Braiding defects reproduces Ising anyon statistics.

Potential applications in topological quantum computing.

Abstract

Anyon models can be symmetric under some permutations of their topological charges. One can then conceive topological defects that, under monodromy, transform anyons according to a symmetry. We study the realization of such defects in the toric code model, showing that a process where defects are braided and fused has the same outcome as if they were Ising anyons. These ideas can also be applied in the context of topological codes.