Universal topological quantum computing via double-braiding in SU(2) Witten-Chern-Simons theory
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909450159259648 |
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| author | Kaufmann, Adrian L. Cui, Shawn X. |
| author_facet | Kaufmann, Adrian L. Cui, Shawn X. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_16747 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universal topological quantum computing via double-braiding in SU(2) Witten-Chern-Simons theory Kaufmann, Adrian L. Cui, Shawn X. Quantum Physics Mathematical Physics Quantum Algebra 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. |
| title | Universal topological quantum computing via double-braiding in SU(2) Witten-Chern-Simons theory |
| topic | Quantum Physics Mathematical Physics Quantum Algebra |
| url | https://arxiv.org/abs/2312.16747 |