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

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.

arXiv comment18 pages; v2: new title, minor corrections and clarifications made

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• Topological phase diagram of $\mathcal{D}(S_3)$ induced by forbidding charges and fluxes