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arXiv · 2509.01423

Quantum Petri Nets with Event Structure semantics

Julien Saan Joachim·Marc de Visme·Stefan Haar·Glynn Winskel
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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.

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Julien Saan Joachim, Marc de Visme, Stefan Haar, Glynn Winskel. 2025-09-01. Quantum Petri Nets with Event Structure semantics. https://arxiv.org/abs/2509.01423

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