Limit theorem for Fibonacci anyons in a pentagon underFmoves

Abstract

In this paper we present an introduction to the theory of anyons and discuss how basis sets and matrix representation of the interaction terms can be obtained, using non-Abelian Fibonacci anyons. We show that the change of basis matrix for certain fusion trees called pentagons is given by a certain unitary matrix which is introduced in Sec. I, and denoted F τ,τ,τ τ throughout the remainder of the paper. We perform a quantum walk with the Fibonacci anyons governed by the unitary matrix F τ,τ,τ τ and obtain the limiting distribution of the walk.