Universal Gates via Fusion and Measurement Operations on SU$(2)_4$ Anyons

TL;DR

This paper demonstrates that fusion and measurement operations on SU(2)_4$ anyons can extend the computational capabilities of braiding, enabling universal quantum computation with topologically protected gates.

Contribution

It introduces a method to achieve universal quantum gates using fusion and measurement on SU(2)_4$ anyons, supplementing braiding operations.

Findings

Fusion and measurement operations generate a universal gate set.

Achieves topologically protected irrational phase gate.

Provides an approximate topologically protected controlled-Z gate.

Abstract

We examine a class of operations for topological quantum computation based on fusing and measuring topological charges for systems with SU$(2)_4$ or $k=4$ Jones-Kauffman anyons. We show that such operations augment the braiding operations, which, by themselves, are not computationally universal. This augmentation results in a computationally universal gate set through the generation of an exact, topologically protected irrational phase gate and an approximate, topologically protected controlled-$Z$ gate.