Quantum Petri Nets with Event Structure semantics

2025-09-01

AI Summary

Existing quantum Petri nets lack rigorous concurrent semantics, unfolding theory, and analytical tools, hindering formal verification of quantum programs. To address this, we propose the first semantically rigorous framework for quantum concurrency: we introduce *local quantum occurrence nets*, the first quantum Petri net model compatible with quantum event structures; define quantum Petri nets with well-defined unfolding semantics; and integrate Clairambault et al.’s quantum event structure model with quantum valuation mechanisms and categorical methods to establish a compositional modeling paradigm. Our main contributions are: (1) establishing a foundational event-structure semantics for quantum concurrency; (2) developing a systematic unfolding theory for quantum Petri nets; and (3) enabling modular modeling and formal analysis of quantum programs—thereby providing essential theoretical underpinnings for quantum software engineering.

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
• Security and Privacy: Data transparency and provenance

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 for quantum concurrency models
• Need semantically grounded quantum concurrency framework

Innovation

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