Topological phases and quantum computation

TL;DR

This paper provides an educational overview of topological phases in low-dimensional quantum systems, emphasizing their relevance to quantum computation and including detailed explanations of models like the toric code and honeycomb model.

Contribution

It offers a pedagogical introduction to topological phenomena in 1-D and 2-D systems, highlighting their significance for quantum computing.

Findings

Introduction to topological phases in 1-D superconductors

Explanation of 2-D topological models like toric code and honeycomb model

Relevance of topological phases to fault-tolerant quantum computation

Abstract

This is a collection of lecture notes from three lectures given by Alexei Kitaev at the 2008 Les Houches summer school "Exact methods in low-dimensional physics and quantum computing." They provide a pedagogical introduction to topological phenomena in 1-D superconductors and in the 2-D topological phases of the toric code and honeycomb model.