Symmetry-restricted quantum circuits are still well-behaved
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arXiv
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| Hauptverfasser: | , , , , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911784070283264 |
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| author | Mansky, Maximilian Balthasar Castillo, Santiago Londoño Armayor-Martínez, Miguel de la Serna, Alejandro Bravo Sathish, Gautham Wang, Zhihao Wölckerlt, Sebastian Linnhoff-Popien, Claudia |
| author_facet | Mansky, Maximilian Balthasar Castillo, Santiago Londoño Armayor-Martínez, Miguel de la Serna, Alejandro Bravo Sathish, Gautham Wang, Zhihao Wölckerlt, Sebastian Linnhoff-Popien, Claudia |
| contents | We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2^n)$, in particular composition, algebraic and topological closedness and connectedness. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space. The well-behavedness is independent of the symmetry requirement imposed on the subgroup. We provide an example of a permutation invariance across all qubits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_16329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetry-restricted quantum circuits are still well-behaved Mansky, Maximilian Balthasar Castillo, Santiago Londoño Armayor-Martínez, Miguel de la Serna, Alejandro Bravo Sathish, Gautham Wang, Zhihao Wölckerlt, Sebastian Linnhoff-Popien, Claudia Quantum Physics We show that quantum circuits restricted by a symmetry inherit the properties of the whole special unitary group $SU(2^n)$, in particular composition, algebraic and topological closedness and connectedness. It extends prior work on symmetric states to the operators and shows that the operator space follows the same structure as the state space. The well-behavedness is independent of the symmetry requirement imposed on the subgroup. We provide an example of a permutation invariance across all qubits. |
| title | Symmetry-restricted quantum circuits are still well-behaved |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.16329 |