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"3-Fermion topological quantum computation", Sam Roberts, Dominic Williamson, 2020

Reviewed August 21, 2023

Citation: Roberts, Sam, and Dominic J. Williamson. "3-fermion topological quantum computation." arXiv preprint arXiv:2011.04693 (2020).

Web: https://indico.physik.uni-muenchen.de/event/84/attachments/244/440/S1A.Roberts.abstract.pdf

Tags: Abelian-anyons

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 K├Ânig. "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.