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Combinatorial optimization problems have attracted much interest in thequantum computing community in the recent years as a potential testbed toshowcase quantum advantage. In this paper, we show how to exploit multilevelcarriers of quantum information -- qudits -- for the construction of algorithmsfor constrained quantum optimization. These systems have been recentlyintroduced in the context of quantum optimization and they allow us to treatmore general problems than the ones usually mapped into qubit systems. Inparticular, we propose a hybrid classical quantum heuristic strategy thatallows us to sample constrained solutions while greatly reducing the searchspace of the problem, thus optimizing the use of fewer quantum resources. As anexample, we focus on the Electric Vehicle Charging and Routing Problem (EVCRP).We translate the classical problem and map it into a quantum system, obtainingpromising results on a toy example which shows the validity of our technique.

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