Essential Unitarity for Higher-Order Quantum Computation

Abstract:We develop a semantic framework for higher-order quantum computation based on a boundary-centric presentation of compact closed categories, building on Kelly--Laplaza and this http URL are polarized boundary linkings composed by execution, with a unit-free monoidal sum providing reversible control and branching. We identify a notion of \emph{essential unitarity} generalizing unitarity from first-order processes to higher-order interfaces;at first order it coincides with standard unitarity, and at higher order it characterizes when information is preserved relative tothe boundary. Essential unitarity is the unique predicate compatible with dagger-monoidal structure, coherence reindexing, and currying, and reducing to ordinary unitarity at first order. Every morphism of the quantum core is essentially unitary. The framework realizes the coherent quantum switch and other one-slot, equal-ratio, purity-preserving supermaps as coherent pure-comb dilations. Extended Abstract appears in QPL 2026

Quantum Physics (quant-ph); Logic in Computer Science (cs.LO); Category Theory (math.CT)

arXiv:2606.04080 [quant-ph]

(or arXiv:2606.04080v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2606.04080 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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