Quantum Petri Nets with Event Structures semantics

TL;DR

This paper introduces Quantum Petri Nets (QPNs), a novel framework that provides a rigorous, semantics-based model for quantum concurrency, bridging Petri net theory and quantum programming.

Contribution

It develops a formal quantum Petri net model with unfolding semantics and a compositional framework, filling a gap in quantum concurrency modeling.

Findings

Defined Quantum Occurrence Nets compatible with quantum event structures

Constructed QPNs with well-defined unfolding semantics

Established a semantically grounded model of quantum concurrency

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.