From Classical to Quantum Optimization: Enhancing Cultural Heritage Visits Through Adaptive Path Planning

The enhancement of cultural heritage through personalized itineraries represents a crucial challenge in the tourism and museum fields. Therefore, this work addresses the problem of maximizing the number of historical-cultural points of interest that can be visited within an archaeological site while respecting constraints on the maximum distance that the visitor can cover. In particular, this study begins with a classical treatment of the problem, highlighting the issues that emerged from a preliminary experimental campaign. Subsequently, the problem is modeled as a combinatorial optimization instance, solvable through a classical-quantum approach based on the Quantum Approximate Optimization Algorithm (QAOA). Thanks to its hybrid structure, QAOA enables the simultaneous exploration of a vast solution space and, through a classical optimizer, updates the parameters of the quantum circuit to converge toward high-performing solutions. The experimental phase utilizes a simulated and simplified environment to evaluate the reliability of the proposed solution and assess its applicability to a real-world case study.