Unitary Designs of Symmetric Local Random Circuits
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866909605286641664 |
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| author | Mitsuhashi, Yosuke Suzuki, Ryotaro Soejima, Tomohiro Yoshioka, Nobuyuki |
| author_facet | Mitsuhashi, Yosuke Suzuki, Ryotaro Soejima, Tomohiro Yoshioka, Nobuyuki |
| contents | We have established the method of characterizing the unitary design generated by a symmetric local random circuit. Concretely, we have shown that the necessary and sufficient condition for the circuit asymptotically forming a t-design is given by simple integer optimization for general symmetry and locality. By using the result, we explicitly give the maximal order of unitary design under the $\mathbb{Z}_2$, U(1), and SU(2) symmetries for general locality. This work reveals the relation between the fundamental notions of symmetry and locality in terms of randomness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unitary Designs of Symmetric Local Random Circuits Mitsuhashi, Yosuke Suzuki, Ryotaro Soejima, Tomohiro Yoshioka, Nobuyuki Quantum Physics Statistical Mechanics We have established the method of characterizing the unitary design generated by a symmetric local random circuit. Concretely, we have shown that the necessary and sufficient condition for the circuit asymptotically forming a t-design is given by simple integer optimization for general symmetry and locality. By using the result, we explicitly give the maximal order of unitary design under the $\mathbb{Z}_2$, U(1), and SU(2) symmetries for general locality. This work reveals the relation between the fundamental notions of symmetry and locality in terms of randomness. |
| title | Unitary Designs of Symmetric Local Random Circuits |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2408.13472 |