Universal Quantum Gate Set from Multiple-Braiding Sequences in $SU(2)_k$ ($k>2$, $k\neq 4$) Anyon Models
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908986401357824 |
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| author | Long, Jiangwei Liu, Zihui Li, Yizhi Zhong, Jianxin Meng, Lijun |
| author_facet | Long, Jiangwei Liu, Zihui Li, Yizhi Zhong, Jianxin Meng, Lijun |
| contents | We study the implementation of a universal quantum gate set via multiple-braiding within $SU(2)_k$ ($k > 2$, $k \neq 4$) anyon models. The multiple elementary braiding matrices (MEBMs) are derived from the $q$-deformed representation theory of $SU(2)$. Braiding multiplicities from one to nine are examined as building blocks for $\{H, T, \text{CNOT}\}$ in $SU(2)_3$ and $SU(2)_5$. Only one case fails to support universality; high-precision $H$ and $T$ gates can be achieved by a Genetic Algorithm enhanced Solovay--Kitaev Algorithm, and expanding operations to 30 enables direct approximation of a locally equivalent CNOT for the remaining eight. Notably, even-order braiding operations offer a physical advantage by reducing the number of non-Abelian anyons required in braiding-based topological quantum computing (TQC). Our numerical results provide strong evidence that most multiple-braiding sequences in $SU(2)_k$ ($k > 2$, $k \neq 4$) anyon models are capable of universal quantum computation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15324 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Universal Quantum Gate Set from Multiple-Braiding Sequences in $SU(2)_k$ ($k>2$, $k\neq 4$) Anyon Models Long, Jiangwei Liu, Zihui Li, Yizhi Zhong, Jianxin Meng, Lijun Quantum Physics We study the implementation of a universal quantum gate set via multiple-braiding within $SU(2)_k$ ($k > 2$, $k \neq 4$) anyon models. The multiple elementary braiding matrices (MEBMs) are derived from the $q$-deformed representation theory of $SU(2)$. Braiding multiplicities from one to nine are examined as building blocks for $\{H, T, \text{CNOT}\}$ in $SU(2)_3$ and $SU(2)_5$. Only one case fails to support universality; high-precision $H$ and $T$ gates can be achieved by a Genetic Algorithm enhanced Solovay--Kitaev Algorithm, and expanding operations to 30 enables direct approximation of a locally equivalent CNOT for the remaining eight. Notably, even-order braiding operations offer a physical advantage by reducing the number of non-Abelian anyons required in braiding-based topological quantum computing (TQC). Our numerical results provide strong evidence that most multiple-braiding sequences in $SU(2)_k$ ($k > 2$, $k \neq 4$) anyon models are capable of universal quantum computation. |
| title | Universal Quantum Gate Set from Multiple-Braiding Sequences in $SU(2)_k$ ($k>2$, $k\neq 4$) Anyon Models |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.15324 |