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## "Twist defects and projective non-Abelian braiding statistics", Maissam Barkeshli, Chao-Ming Jian, Xiao-Liang Qi, 2013

*Reviewed January 2, 2024*

*Citation:* Barkeshli, Maissam, Chao-Ming Jian, and Xiao-Liang Qi. "Twist defects and projective non-Abelian braiding statistics." Physical Review B 87.4 (2013): 045130.

*Web:* https://arxiv.org/abs/1208.4834

*Tags:* Defects/Boundaries, Ising-computer, Universal-scheme, Modular-tensor-categories

This paper discusses the layer interchange symmetry in bilayer topological phases.
Specifically, it discusses the class of defects which can be introduced to realize these symmetries.
The main result of the paper is that these layer-exchange defects behave exactly the same
as adding genus to the surface, and braiding them results in mapping class group actions.
The paper coins the term *genons* for these defects.

Using this general theory, the authors then give an explicit protocol
for universal quantum computing with defects in bilayer Ising anyons.