Quantum computation with abelian anyons

TL;DR

This paper demonstrates that abelian anyons can be used to construct a universal quantum computer, performing all logic operations through topological effects and single-anyon manipulations, with some robustness advantages.

Contribution

It introduces a method for quantum computation using abelian anyons, showing how to implement universal gates with topological effects and single-anyon operations.

Findings

Universal quantum computation is possible with abelian anyons.

Controlled-NOT and other gates can be realized via topological effects.

Abelian anyon-based quantum computing shares partial robustness with non-abelian systems.

Abstract

A universal quantum computer can be constructed using abelian anyons. Two qubit quantum logic gates such as controlled-NOT operations are performed using topological effects. Single-anyon operations such as hopping from site to site on a lattice suffice to perform all quantum logic operations. Quantum computation using abelian anyons shares some but not all of the robustness of quantum computation using non-abelian anyons.