A Modeling approach based on Coloured Petri Nets for Quantum algorithm

Verifying the correctness of quantum algorithms and reducing the understanding threshold are important parts of quantum computing. Formal methods, as effective techniques, are increasingly being focused on for these purpose. Given the superposition and entanglement of quantum algorithms, reasonably and intuitively formalizing them is a big challenge. In our work, Coloured Petri Nets (CPN), a sophisticated extension of Petri nets, are harnessed to represent the quantum states in the Hilbert space, the formal approach based on CPN for quantum algorithms is proposed in this paper. Then, the process of constructing a CPN quantum model is demonstrated using the modeling of the Deutsch algorithm, simulations of the algorithm are conducted within the model, with intermediate quantum states being recorded, and the simulation results subsequently analyzed. The quantum properties of Deutsch algorithm such as superposition and entanglement among quantum states can be formalized reasonably, demonstrating the rationality and effectiveness of the model in this paper. Finally, this paper verifies the model’s capability in modeling complex-valued operations of entangled qubits through the construction of a simple circuit.