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arXiv · 2312.16747

Universal topological quantum computing via double-braiding in SU(2) Witten-Chern-Simons theory

Adrian L. Kaufmann·Shawn X. Cui
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Abstract

We study the problem of universality in the anyon model described by the $SU(2)$ Witten-Chern-Simons theory at level $k$. A classic theorem of Freedman-Larsen-Wang states that for $k \geq 3, \ k \neq 4$, braiding of the anyons of topological charge $1/2$ is universal for topological quantum computing. For the case of one qubit, we prove a stronger result that double-braiding of such anyons alone is already universal.

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Adrian L. Kaufmann, Shawn X. Cui. 2023-12-27. Universal topological quantum computing via double-braiding in SU(2) Witten-Chern-Simons theory. https://doi.org/10.1007/s11128-024-04633-1

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