A Quantum Net

Julien Saan Joachim, Marc de Visme, Stefan Haar +1 more

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.

Julien Saan Joachim, Marc de Visme, Stefan Haar

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.

Forrest Landry

Kong, Liang, Hao Zheng

We continue our study of the categories of quantum liquids started in a previous work. We combine local quantum symmetries with topological skeletons into a single mathematical theory of topological nets and defect nets. In particular, we introduce the notion of a topological net, which is motivated from and generalizes that of a conformal net, and the notion of a defect net which generalizes that of a defect between conformal nets. We give explicit examples of them. Moreover, we construct the category of topological $n$-nets with $k$-morphisms defined by defect $n$-nets of codimension $k$, and show that the category of $n$D quantum liquids can be extracted from it and computed explicitly via the condensation theory of topological nets.