Denotational Semantics for Higher-Order Quantum Symmetric Pattern-Matching

Develop a denotational semantics for the full higher-order quantum fragment of symmetric pattern-matching, providing a sound and adequate categorical model for higher-order quantum operations in that language.

Background

Symmetric pattern-matching is presented as a typed language for reversible and quantum programming. Existing results furnish denotational semantics and adequacy for its higher-order classical reversible fragment, and a complete denotational semantics for its first-order quantum fragment.

The authors explicitly note that a denotational semantics for the full higher-order quantum version remains unresolved, and later discuss how guarded recursion might help address issues such as structural recursion in the quantum setting.