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.

中文翻译：

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如何将量子烘焙到您的宠物 Petri 网中并拥有您的网络理论

Petri 网已在许多应用程序领域中得到广泛使用，尤其是由于其基于偏序依赖性和并发执行的交互分布式和异步进程和服务的组合的人性化图形语法。Petri 网还带有抽象语义，以及用于组合综合、结构检查和行为分析的数学方法。这些已经导致将各种网络用于实时、分布式和并行编程语言、软件和服务系统，以查看它们的接口和交互协议。这些可供性使得 Petri 网对于专注于组件、它们的相互依赖和面向环境的交互的分布式软件架构方法非常宝贵。量子计算——尤其是量子软件工程——正处于起步阶段，可以从软件架构研究和网络理论、方法和应用的积累见解中受益。在本文中，我们建立了 Petri 网和量子系统之间的联系，这样网络理论和网络的组件体系结构可以帮助合成和分析抽象软件模型及其在混合经典和量子编程语言中的接口协议和服务系统。我们利用来自软件规范的网络形式的一些见解，将量子烘焙成现存的 Petri 网风味，并证明 Petri 网在量子编程中的普遍性和组合性。