Topological Quantum Computing

TL;DR

This paper provides an overview of topological quantum computing, focusing on anyons, Majorana fermions, and their potential for universal quantum computation, based on lecture notes from a 2017 school.

Contribution

It offers a comprehensive introduction to the theoretical foundations and practical aspects of topological quantum computing, including models and computational schemes.

Findings

Explains abelian and non-abelian anyons and their realization in models.

Describes how to perform universal quantum computation with Majorana fermions.

Provides foundational knowledge for future research in topological quantum computing.

Abstract

This set of lecture notes forms the basis of a series of lectures delivered at the 48th IFF Spring School 2017 on Topological Matter: Topological Insulators, Skyrmions and Majoranas at Forschungszentrum Juelich, Germany. The first part of the lecture notes covers the basics of abelian and non-abelian anyons and their realization in the Kitaev's honeycomb model. The second part discusses how to perform universal quantum computation using Majorana fermions.