How to Bake Quantum into Your Pet Petri Nets and Have Your Net Theory Too.

Petri nets have found widespread use among many application domains, not least due to their human-friendly graphical syntax for the composition of interacting distributed and asynchronous processes and services, based in partial-order dependencies and concurrent executions. Petri nets also come with abstract semantics, and mathematical methods for compositional synthesis, structural checks and behavioural analysis. These have led to the use of various kinds of nets for real-time, distributed and parallel programming languages, software and services systems, with a view to their interfaces and interaction protocols. These affordances make Petri nets invaluable for distributed software architecture approaches focused on components, their mutual dependencies and environment-facing interactions. Quantum computing -- and in particular quantum software engineering -- is in its infancy and could benefit from the accumulated insights of software architecture research and of net theory, its methods, and its applications. In this paper, we establish a connection between Petri nets and quantum systems, such that net theory and the component architecture of nets may help in the synthesis and analysis of abstract software models and their interface protocols in hybrid classical-and-quantum programming languages and services systems. We leverage some insights from net formalisms for software specification for a versatile recipe to bake quantum into extant Petri net flavours, and prove universality and compositionality of Petri nets for quantum programming.