An Invitation to the Mathematics of Topological Quantum Computation

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.

10 figures, 1 table. Submitted to the proceeding of Quantumfest 2015. Dedicated to the memory of Sujeev Wickramasekara