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Citation: Roberts, Sam, and Dominic J. Williamson. "3-fermion topological quantum computation." arXiv preprint arXiv:2011.04693 (2020).
This paper shows that the (abelian) "3-fermion" MTC obtains the full Clifford group by braiding alone, if you store information in the correct way. Their model works in (3+1) dimensions, fitting into the general "Walker-Wang" paradigm:
> Walker, Kevin, and Zhenghan Wang. "(3+ 1)-TQFTs and topological insulators." Frontiers of Physics 7 (2012): 150-159.
The fact that (3+1)-dimensional abelian anyonic theories can implement the Clifford group by braiding alone is not surprising. It is entirely within the expected Bravyi-Konig bound:
>Bravyi, Sergey, and Robert König. "Classification of topologically protected gates for local stabilizer codes." Physical review letters 110.17 (2013): 170503.
The paper is not very professionally written, but it seems to contain a lot of interesting ideas.