Large $k$ topological quantum computer

• URL: http://arxiv.org/abs/2105.03980v2
• Date: Tue, 8 Feb 2022 20:10:29 GMT
• Title: Large $k$ topological quantum computer
• Abstract summary: Chern-Simons topological quantum computer is a device that can be effectively described by the Chern-Simons topological quantum field theory. Quantum qudit gates of this quantum computer are represented by sequences of quantum $mathcalR$-matrices.
• Score: 0.7734726150561089
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Chern-Simons topological quantum computer is a device that can be effectively described by the Chern-Simons topological quantum field theory and used for quantum computations. Quantum qudit gates of this quantum computer are represented by sequences of quantum $\mathcal{R}$-matrices. Its dimension and explicit form depend on the parameters of the Chern-Simons theory -- level $k$, gauge group $SU(N)$, and representation, which is chosen to be symmetric representation $[r]$. In this paper, we examine the universality of such a quantum computer. We prove that for sufficiently large $k$ it is universal, and the minimum allowed value of $k$ depends on the remaining parameters $r$ and $N$.

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