Citation: Delaney, Colleen, and Zhenghan Wang. "Symmetry defects and their application to topological quantum computing." Contemporary Mathematics (2020): 121-151.
Web: https://arxiv.org/abs/1811.02143
Tags: Ising-computer, SPT/SETs, Expository
This paper gives a mathematical treatment of symmetry defects, with a focus on their application to quantum computing. While nothing in this paper is new, it is a good reference for people wanting to learn the subject.
An important point in this paper is that it puts the work of
> Barkeshli, Maissam, Chao-Ming Jian, and Xiao-Liang Qi. "Twist defects and projective non-Abelian braiding statistics." Physical Review B—Condensed Matter and Materials Physics 87.4 (2013): 045130.
on firm mathematical footing. The results of Barkeshli et al. imply a very specific structure on genons in bilayer Ising. When Colleen and Zhenghan looked at it mathematically, however, they realized they could not come up with a proof! That is, the results of Barkeshli et al. do NOT serve as a proof that genons in Ising lead to universal quantum computation - Barkseshli et al.'s result paired with the work in this paper establish that genons in Ising CONJECTURALLY are univeral, with the open part being a question about the skeletal symbols of genons in Ising.