Generalized Color Codes Supporting Non-Abelian Anyons

TL;DR

This paper introduces a generalized framework for color codes based on finite groups, enabling the support of non-abelian anyons and topological order, expanding the scope of quantum error correction and topological quantum computation.

Contribution

It presents a novel generalization of color codes using finite groups, particularly non-abelian groups, linking them to Kitaev quantum double models and exploring their quasiparticle properties.

Findings

Supports non-abelian anyonic quasiparticles

Establishes relationship to Kitaev quantum double models

Analyzes boundary structures and quasiparticle spectrum

Abstract

We propose a generalization of the color codes based on finite groups $G$. For non-abelian groups, the resulting model supports non-abelian anyonic quasiparticles and topological order. We examine the properties of these models such as their relationship to Kitaev quantum double models, quasiparticle spectrum, and boundary structure.