Exotic non-Abelian anyons from conventional fractional quantum Hall states

TL;DR

This paper proposes a device using fractional quantum Hall states and superconductors to realize and manipulate non-Abelian parafermions, advancing quantum computing potential with experimentally feasible methods.

Contribution

It introduces a novel device platform supporting parafermions in fractional quantum Hall systems, with practical methods for detection and braiding, enhancing non-Abelian anyon research.

Findings

Parafermions can be supported in fractional quantum Hall-superconductor devices.

Josephson measurements can distinguish parafermions from Majoranas.

Braiding parafermions yields richer topological qubit operations.

Abstract

Non-Abelian anyons--particles whose exchange noncommutatively transforms a system's quantum state--are widely sought for the exotic fundamental physics they harbor as well as for quantum computing applications. There now exist numerous blueprints for stabilizing the simplest type of non-Abelian anyon, defects binding Majorana modes, by judiciously interfacing widely available materials. Following this line of attack, we introduce a device fabricated from conventional fractional quantum Hall states and s-wave superconductors that supports exotic non-Abelian anyons that bind `parafermions', which can be viewed as fractionalized Majorana fermions. We show that these modes can be experimentally identified (and distinguished from Majoranas) using Josephson measurements. We also provide a practical recipe for braiding parafermions and show that they give rise to non-Abelian statistics. Interestingly, braiding in our setup produces a richer set of topologically protected qubit operations when compared to the Majorana case. As a byproduct, we establish a new, experimentally realistic Majorana platform in weakly spin-orbit-coupled materials such as GaAs.