A categorical approach to quantum computation with anyons

Abstract

[en] Topological quantum computation is an approach to quantum computation that employs exotic quasiparticles, called anyons, to store and manipulate quantum information. Anyons can be mathematically described by a unitary modular tensor category. In this work, we give an overview of the relevant category theory necessary to introduce an anyon model, as well as the structures used in computing processes. Having developed all the necessary theoretical background, we introduce the Fibonacci anyon model, the simplest model that can give rise to universal quantum computation. Moreover, we describe how quantum computation could be carried out within such model.