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: Higher-dimensional, Abelian-anyons, Universal-scheme
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.
This paper contains a lot of interesting ideas, and is a good reference for the 3-fermion model, which become a staple of the field. The original reference for the 3-fermion model goes back to 2009:
> Bombin, Hector, M. Kargarian, and M. A. Martin-Delgado. "Interacting anyonic fermions in a two-body color code model." Physical Review B 80.7 (2009): 075111.
The original 3 fermion model lives in 2+1 dimensions. It it is a theory with 4 simple objects. All three non-trivial simple objects are fermions, hence the name. This theory also goes by the name of the (D4,1) model, as included in the table in
> Rowell, Eric, Richard Stong, and Zhenghan Wang. "On classification of modular tensor categories." Communications in Mathematical Physics 292.2 (2009): 343-389.
A nice Hamiltonian realization of the (2+1)-dimensional dimensional 3 fermion model is given in
> Bombín, Héctor. "Topological subsystem codes." Physical review A 81.3 (2010): 032301.
The fact that this paper deals also with (3+1)-dimensional is not very important, and much of the paper also deals with (2+1)-dimensional 3-fermionic phenomena.