On the Reachability Problem in Quantum Petri Nets

Abstract

In this paper, we propose a novel quantum solution to address the problem of reachability in bounded quantum Petri nets (QPNs), an advanced modeling framework that combines the classical Petri net model with quantum mechanical principles. The proposed approach exploits quantum parallelism to construct a superposition over all reachable markings from the initial marking. Grover's amplitude amplification algorithm is then applied to efficiently identify a desired target marking, while ancillary q-tokens used solely for transition control are excluded from the search space, significantly reducing its size. Theoretical analysis shows that our approach achieves a quadratic speed up over classical exhaustive algorithms. Experimental results also confirm the correctness and feasibility of the proposed quantum algorithm for solving the bounded reachability problem in Quantum Petri Nets.