Citation: Levaillant, Claire, et al. "Universal gates via fusion and measurement operations on SU (2) 4 anyons." Physical Review A 92.1 (2015): 012301.
Web: https://arxiv.org/abs/1504.02098
Tags: Modular-tensor-categories, Universal-scheme
There is a general theme in topological quantum computation that any topological phase can be made universal if you try hard enough. This paper is case in point of that theme. k=2,4 are the special values where SU(2)_k anyons are not universal by braiding alone. But, if you try hard enough with k=4 anyons, this paper shows you can get a universal gate set! The extra operations come from fusing anyons and coherently measuring topological charges as a computational primitive instead of just as a state preparation and readout technique, just like Mochon did for finite groups:
> Mochon, Carlos. "Anyons from nonsolvable finite groups are sufficient for universal quantum computation." Physical Review A 67.2 (2003): 022315.
The scheme introduced in this paper also works with Jones-Kauffman anyons at level k=4, which are related to but not equal to SU(2)_4 anyons.