Braiding of non-Abelian anyons using pairwise interactions

TL;DR

This paper proposes an alternative method for braiding non-Abelian anyons in topological quantum computation by adiabatically varying pairwise interactions rather than physically moving the anyons, potentially enhancing control and protection.

Contribution

It introduces a scheme to realize anyonic braiding through adiabatic tuning of pairwise couplings, offering a new approach to topological quantum gates.

Findings

Braiding operators can be implemented via adiabatic cycles in coupling space.

A T-junction system with four anyons demonstrates the method.

Coupling with anyonic chains can preserve topological protection.

Abstract

The common approach to topological quantum computation is to implement quantum gates by adiabatically moving non-Abelian anyons around each other. Here we present an alternative perspective based on the possibility of realizing the exchange (braiding) operators of anyons by adiabatically varying pairwise interactions between them rather than their positions. We analyze a system composed by four anyons whose couplings define a T-junction and we show that the braiding operator of two of them can be obtained through a particular adiabatic cycle in the space of the coupling parameters. We also discuss how to couple this scheme with anyonic chains in order to recover the topological protection.