Geometrical approach to SU(2) navigation with Fibonacci anyons

TL;DR

This paper introduces a geometrical method for approximating SU(2) unitary transformations in topological quantum computation with Fibonacci anyons, offering an alternative to the Solovay-Kitaev algorithm.

Contribution

It presents a novel geometrical approach based on a generalization of the geodesic dome construction for SU(2), improving approximation techniques in topological quantum computing.

Findings

Provides an efficient approximation method for SU(2) unitaries

Demonstrates the method's applicability to Fibonacci anyon braiding

Offers an alternative to the Solovay-Kitaev algorithm

Abstract

Topological quantum computation with Fibonacci anyons relies on the possibility of efficiently generating unitary transformations upon pseudoparticles braiding. The crucial fact that such set of braids has a dense image in the unitary operations space is well known; in addition, the Solovay-Kitaev algorithm allows to approach a given unitary operation to any desired accuracy. In this paper, the latter task is fulfilled with an alternative method, in the SU(2) case, based on a generalization of the geodesic dome construction to higher dimension.