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

• URL: http://arxiv.org/abs/2312.16747v1
• Date: Wed, 27 Dec 2023 23:49:22 GMT
• Title: Universal topological quantum computing via double-braiding in SU(2) Witten-Chern-Simons theory
• Abstract summary: We show 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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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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