Sequential quantum processes with group symmetries

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 $U\in \mathrm{SU}(d)$ into 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 $U$.

arXiv:2510.07100 [quant-ph]

(or arXiv:2510.07100v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2510.07100 Focus to learn more arXiv-issued DOI via DataCite

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