Quantum Petri Nets with Event Structure semantics
Abstract
Classical Petri nets provide a canonical model of concurrency, with unfolding semantics linking nets, occurrence nets, and event structures. No comparable framework exists for quantum concurrency: existing ''quantum Petri nets'' lack rigorous concurrent and sound quantum semantics, analysis tools, and unfolding theory. We introduce Quantum Petri Nets (QPNs), Petri nets equipped with a quantum valuation compatible with the quantum event structure semantics of Clairambault, De Visme, and Winskel (2019). Our contributions are: (i) a local definition of Quantum Occurrence Nets (LQONs) compatible with quantum event structures, (ii) a construction of QPNs with a well-defined unfolding semantics, (iii) a compositional framework for QPNs. This establishes a semantically well grounded model of quantum concurrency, bridging Petri net theory and quantum programming.
Keywords
Cite
@article{arxiv.2509.01423,
title = {Quantum Petri Nets with Event Structure semantics},
author = {Julien Saan Joachim and Marc de Visme and Stefan Haar and Glynn Winskel},
journal= {arXiv preprint arXiv:2509.01423},
year = {2025}
}