Majorana Zero Modes and Topological Quantum Computation

TL;DR

This paper reviews the theoretical and experimental progress in Majorana zero modes within solid state systems, highlighting their potential for topological quantum computation through braiding-based operations and recent experimental signatures.

Contribution

It provides a comprehensive overview of recent experimental evidence, theoretical analyses, and proposed schemes for utilizing Majorana zero modes in topological quantum computing.

Findings

Experimental signatures consistent with Majorana modes in nanowires

Discussion of non-Abelian braiding statistics for quantum gates

Analysis of fractional quantum Hall systems related to Majorana modes

Abstract

We provide a current perspective on the rapidly developing field of Majorana zero modes in solid state systems. We emphasize the theoretical prediction, experimental realization, and potential use of Majorana zero modes in future information processing devices through braiding-based topological quantum computation. Well-separated Majorana zero modes should manifest non-Abelian braiding statistics suitable for unitary gate operations for topological quantum computation. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localized at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic Majorana zero modes in solid state systems. We also discuss fractional quantum Hall systems (the 5/2 state) in this context. We describe proposed schemes for carrying out braiding with Majorana zero modes as well as the necessary steps for implementing topological quantum computation.