Formulation of the Electric Vehicle Charging and Routing Problem for a Hybrid Quantum-Classical Search Space Reduction Heuristic

Combinatorial optimization problems have attracted much interest in the quantum computing community in the recent years as a potential testbed to showcase quantum advantage. In this paper, we show how to exploit multilevel carriers of quantum information -- qudits -- for the construction of algorithms for constrained quantum optimization. These systems have been recently introduced in the context of quantum optimization and they allow us to treat more general problems than the ones usually mapped into qubit systems. In particular, we propose a hybrid classical quantum heuristic strategy that allows us to sample constrained solutions while greatly reducing the search space of the problem, thus optimizing the use of fewer quantum resources. As an example, we focus on the Electric Vehicle Charging and Routing Problem (EVCRP). We translate the classical problem and map it into a quantum system, obtaining promising results on a toy example which shows the validity of our technique.