Universal Quantum Computation with Abelian Anyon Models

TL;DR

This paper demonstrates that adding non-topological operations to abelian anyon models enables universal quantum computation while maintaining topological protection, bridging the gap between abelian and non-abelian models.

Contribution

It shows that non-topological operations like spin measurements can make abelian anyon models universal for quantum computation.

Findings

Non-topological operations enable universality in abelian models

Topological protection is preserved with additional operations

Provides insights into abelian and non-abelian model relations

Abstract

We consider topological quantum memories for a general class of abelian anyon models defined on spin lattices. These are non-universal for quantum computation when restricting to topological operations alone, such as braiding and fusion. The effects of additional non-topological operations, such as spin measurements, are studied. These are shown to allow universal quantum computation, while still utilizing topological protection. Our work gives an insight into the relation between abelian models and their non-abelian counterparts.