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Citation: Laubscher, Katharina, Daniel Loss, and James R. Wootton. "Universal quantum computation in the surface code using non-Abelian islands." Physical Review A 100.1 (2019): 012338.
This paper introduces a method for universal quantum computation in the surface code. Namely, there are small "islands" of non-abelian anyons. These islands are used as factories with which to create states which the surface code can then use for universal quantum computation.
I am a bit confused, because the non-abelian universal power of S3 seems like way too much. The ability to transfer between surface codes with domain boundaries is already a lot. Namely, if you had abelian Z4 islands (without a doubt the simplest anyons to implement after Z2), then it seems to me like a domain boundary would allow for the implementation of the "F-gate" from
>Moussa, Jonathan E. "Quantum circuits for qubit fusion." arXiv preprint arXiv:1512.06132 (2015).
And hence would allow for universal quantum computation. I'm not sure though, I need to work out the details...