A Lie-algebraic Criterion for the Universality of Exponentiated Quantum Gates
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866913070825078784 |
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| author | Xue, Yinuo Chen, Qian Huang, Jing-Song |
| author_facet | Xue, Yinuo Chen, Qian Huang, Jing-Song |
| contents | We present a criterion that serves as the basis for a polynomial-time algorithm to decide whether a finite set of qudit gates exponentiated by some Hamiltonians is universal. Our approach formulates universality in Lie algebraic terms and applies Borel--de Siebenthal theory with a diagonal generator having incommensurate spectrum. In this framework, nonuniversality is detected by invariant subspaces, equivalently by a graph-connectivity obstruction, while universality is repaired by adding generators that couple disconnected components. We further prove that two generators are sufficient for universal control. Our work reveals a profound link between qudit universality and irreducibility of Lie algebra representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_25971 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Lie-algebraic Criterion for the Universality of Exponentiated Quantum Gates Xue, Yinuo Chen, Qian Huang, Jing-Song Quantum Physics We present a criterion that serves as the basis for a polynomial-time algorithm to decide whether a finite set of qudit gates exponentiated by some Hamiltonians is universal. Our approach formulates universality in Lie algebraic terms and applies Borel--de Siebenthal theory with a diagonal generator having incommensurate spectrum. In this framework, nonuniversality is detected by invariant subspaces, equivalently by a graph-connectivity obstruction, while universality is repaired by adding generators that couple disconnected components. We further prove that two generators are sufficient for universal control. Our work reveals a profound link between qudit universality and irreducibility of Lie algebra representations. |
| title | A Lie-algebraic Criterion for the Universality of Exponentiated Quantum Gates |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.25971 |