Designer non-Abelian anyon platforms: from Majorana to Fibonacci

TL;DR

This paper reviews progress in creating non-Abelian anyons, including Majorana, parafermionic, and Fibonacci types, through engineered structures, highlighting their potential for fault-tolerant quantum computing and experimental exploration.

Contribution

It unifies strategies for realizing various non-Abelian anyons in quantum Hall systems and discusses their implications for universal quantum computation.

Findings

Progress in trapping Majorana zero modes in engineered structures

Proposal of interfacing quantum Hall systems with superconductors for exotic anyons

Identification of experimental opportunities for discovering Fibonacci anyons

Abstract

The emergence of non-Abelian anyons from large collections of interacting elementary particles is a conceptually beautiful phenomenon with important ramifications for fault-tolerant quantum computing. Over the last few decades the field has evolved from a highly theoretical subject to an active experimental area, particularly following proposals for trapping non-Abelian anyons in `engineered' structures built from well-understood components. In this short overview we briefly tour the impressive progress that has taken place in the quest for the simplest type of non-Abelian anyon---defects binding Majorana zero modes---and then turn to similar strategies for pursuing more exotic excitations. Specifically, we describe how interfacing simple quantum Hall systems with conventional superconductors yields `parafermionic' generalizations of Majorana modes and even Fibonacci anyons---the latter enabling fully fault tolerant universal quantum computation. We structure our treatment in a manner that unifies these topics in a coherent way. The ideas synthesized here spotlight largely uncharted experimental territory in the field of quantum Hall physics that appears ripe for discovery.