Quantum Computing with $\mathbb{Z}_2$ Abelian anyon system

TL;DR

This paper proposes a novel topological quantum computing approach using a $ ext{Z}_2$ abelian anyon system with defects, challenging the belief that only non-abelian systems can support such computation.

Contribution

It introduces a prototype for topological quantum computing based on abelian anyon systems, expanding the scope beyond non-abelian models.

Findings

Demonstrates a $ ext{Z}_2$ abelian anyon system can support quantum computation

Provides a prototype implementation of abelian topological quantum computer

Challenges the belief that only non-abelian anyons enable topological quantum computing

Abstract

Topological quantum computers provide a fault-tolerant method for performing quantum computation. Topological quantum computers manipulate topological defects with exotic exchange statistics called anyons. The simplest anyon model for universal topological quantum computation is the Fibonacci anyon model, which is a non-abelian anyon system. In non-abelian anyon systems, exchanging anyons always results a unitary operations instead of a simple phase changing in abelian anyon systems. So, non-abelian anyon systems are of the interest to topological quantum computation. Up till now, most people still hold the belief that topological quantum computions can be implemented only on the non-abelian anyon systems. But actually this is not true. Inspired by extrinsic semiconductor technology, we suggest that abelian anyon systems with defects also support topological quantum computing. In this letter, we report a topological quantum computer prototype based on $\mathbb{Z}_2$ abelian anyon system.