Sequential quantum processes with group symmetries
Fuente:
arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912636156772352 |
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| author | Grinko, Dmitry Yoshida, Satoshi Murao, Mio Ozols, Maris |
| author_facet | Grinko, Dmitry Yoshida, Satoshi Murao, Mio Ozols, Maris |
| contents | Symmetry plays a crucial role in the design and analysis of quantum protocols. This result shows a canonical circuit decomposition of a $(G \times H)$-invariant quantum comb for compact groups $G$ and $H$ using the corresponding Clebsch-Gordan transforms, which naturally extends to the $G$-covariant quantum comb. By using this circuit decomposition, we propose a parametrized quantum comb with group symmetry, and derive the optimal quantum comb which transforms an unknown unitary operation $U \in \mathrm{SU}(d)$ to its inverse $U^\dagger$ or transpose $U^\top$. From numerics, we find a deterministic and exact unitary transposition protocol for $d=3$ with $7$ queries to $U$. This protocol improves upon the protocol shown in the previous work, which requires $13$ queries to $U$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_07100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sequential quantum processes with group symmetries Grinko, Dmitry Yoshida, Satoshi Murao, Mio Ozols, Maris Quantum Physics Symmetry plays a crucial role in the design and analysis of quantum protocols. This result shows a canonical circuit decomposition of a $(G \times H)$-invariant quantum comb for compact groups $G$ and $H$ using the corresponding Clebsch-Gordan transforms, which naturally extends to the $G$-covariant quantum comb. By using this circuit decomposition, we propose a parametrized quantum comb with group symmetry, and derive the optimal quantum comb which transforms an unknown unitary operation $U \in \mathrm{SU}(d)$ to its inverse $U^\dagger$ or transpose $U^\top$. From numerics, we find a deterministic and exact unitary transposition protocol for $d=3$ with $7$ queries to $U$. This protocol improves upon the protocol shown in the previous work, which requires $13$ queries to $U$. |
| title | Sequential quantum processes with group symmetries |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.07100 |