Year: 2026
Type: preprint
Abstract: We introduce a graded graph-series semantics for recursive hybrid quantum programs interpreted in the quantum orchestra monad. Finite terminating executions are represented by directed paths whose edges carry normal completely positive subunital maps and whose terminal vertices carry classical results. Path concatenation defines a graded execution category, while continuation grafting models outcome-dependent sequential composition. We construct a semantic evaluation from admissible execution-graph series to quantum orchestras and prove that it is compatible with both channel composition and Kleisli composition. For finitary recursive programs, the truncation of the execution series at degree $n$ is shown to coincide with the $n$-th Kleene approximant of the associated Scott-continuous recursion functional. Consequently, evaluation of the complete graph series recovers the ordinary least-fixed-point denotation. Weighting a graph of degree $n$ by $q^n$, with $0
Source: arXiv (Cornell University)
Author: Magnot, Jean-Pierre
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169019595
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