An Invitation to the Mathematics of Topological Quantum Computation

TL;DR

This paper discusses the mathematical foundations and recent advances in topological quantum computation, emphasizing its potential for decoherence-resistant quantum computing and exploring extensions to three-dimensional materials.

Contribution

It provides a mathematician's perspective on topological quantum computation, highlighting recent progress and proposing extensions to three-dimensional topological states.

Findings

Topological states offer decoherence protection for quantum computing

Recent mathematical advances improve understanding of topological quantum systems

Extension of theory to three-dimensional materials is feasible

Abstract

Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematician's perspective on some of the advantages and challenges of this model, highlighting some recent advances. We then give a short description of how we might extend the theory to three-dimensional materials.