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.
Web: https://arxiv.org/pdf/1811.06738.pdf
Tags: Universal-scheme, Defects/boundaries, Toric-code
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.
One way to extend these results would be to replace S3 with a simpler phase. 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.