Sequential quantum processes with group symmetries

• URL: http://arxiv.org/abs/2510.07100v1
• Date: Wed, 08 Oct 2025 14:58:08 GMT
• Title: Sequential quantum processes with group symmetries
• Authors: Dmitry Grinko, Satoshi Yoshida, Mio Murao, Maris Ozols,
• Abstract summary: We show a canonical circuit decomposition of a $(G times H)$-invariant quantum comb for compact groups $G$ and $H$.<n>We derive the optimal quantum comb which transforms an unknown unitary operation $U in mathrmSU(d)$ to its inverse $Udagger$ or transpose $Utop$.
• Score: 0.23332469289621782
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $U$.

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