Universal gates via fusion and measurement operations on SU (2) 4 anyons

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.