Quantum Petri Nets with Event Structures semantics

2025-08-20

AI Summary

Existing quantum Petri net models lack rigorous concurrent semantics, well-defined unfolding theories, and effective analysis tools. Method: We propose the first quantum Petri net framework endowed with a formal quantum event structure semantics; we introduce local quantum occurrence nets and define a compositional, unfoldable, and semantically sound model by integrating Clairambault–De Visme–Winskel’s quantum event structures with classical Petri net concurrency principles, underpinned by quantum valuations and unfolding techniques. Contribution/Results: This framework bridges critical gaps in quantum concurrency theory—specifically, in semantic rigor, compositional modeling, and support for static analysis. It provides a foundational modeling infrastructure for formal verification and behavioral analysis of quantum programs, enabling precise reasoning about quantum parallelism, entanglement, and non-deterministic quantum evolution.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Models for Web evolution

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.

Problem

• Lack rigorous concurrent semantics for quantum Petri nets
• Absence of unfolding theory in quantum concurrency models
• Need compositional framework for quantum Petri nets

Innovation

• Quantum Petri Nets with quantum valuation
• Local Quantum Occurrence Nets definition
• Compositional framework with unfolding semantics