Acyclic anyon models, thermal anyon error corrections, and braiding universality

TL;DR

This paper characterizes acyclic non-abelian anyon models, explores their error correction capabilities, and investigates their relation to computational universality, introducing new models like $SO(8)_2$ and certain Dijkgraaf-Witten theories.

Contribution

It provides a comprehensive characterization of acyclic anyon models and identifies new models, raising questions about their computational significance and limitations.

Findings

Acyclic models can correct thermal anyon errors.

New acyclic models such as $SO(8)_2$ and nilpotent Dijkgraaf-Witten theories are identified.

Open questions about the computational power of acyclic models are raised.

Abstract

Acyclic anyon models are non-abelian anyon models for which thermal anyon errors can be corrected. In this note, we characterize acyclic anyon models and raise the question if the restriction to acyclic anyon models is a deficiency of the current protocol or could it be intrinsically related to the computational power of non-abelian anyons. We also obtain general results on acyclic anyon models and find new acyclic anyon models such as $SO(8)_2$ and untwisted Dijkgraaf-Witten theories of nilpotent finite groups.