# Models for non-universal topological quantum computation

Anyon models do not lead in general to universal topological quantum computation (= existence of a universal set of quantum gates) when only the braiding is used for implementing gates. The Fibonacci anyon model has been shown to be universal for quantum computation (see e.g. http://www.thp.uni-koeln.de/trebst/pubs/FibonacciAnyonModels.pdf for an overview), as are all $\mathrm{SU}(2)_k$-models with $k>2$, $k\neq 4$ (https://arxiv.org/abs/math/0103200), while the Ising model is not (in https://arxiv.org/abs/1208.4834 it is shown that a bilayer Ising model can be made universal when introducing permutation defects).

Question: Are there any other known anyon models besides the Ising model which are non-universal when only the braiding is used? I am particularly interested in models of non-abelian anyons. (Please provide literature sources when answering this question!)

• In general, abelian anyon models are not universal. – AccidentalFourierTransform May 10 '18 at 13:39
• @AccidentalFourierTransform What about non-abelian anyons? And could you please state the research papers involved? – kolaka May 10 '18 at 17:54
• see e.g. arxiv.org/abs/0904.4373 – AccidentalFourierTransform May 10 '18 at 19:19