On quantum computation, anyons, and categories

TL;DR

This paper explores how category theory can describe anyons, especially Fibonacci anyons, simplifying their mathematical framework and providing explicit calculations that enhance understanding for researchers.

Contribution

It introduces a simplified categorical approach to describing anyons and presents explicit calculations for Fibonacci anyons not previously detailed in literature.

Findings

Category theory effectively describes certain anyons.

Simplification of the mathematical description via Yoneda's lemma.

Explicit calculations for Fibonacci anyons are provided.

Abstract

We explain the use of category theory in describing certain sorts of anyons. Yoneda's lemma leads to a simplification of that description. For the particular case of Fibonacci anyons, we also exhibit some calculations that seem to be known to the experts but not explicit in the literature.