Quantum-Classical Framework for the Joint Optimization of Bidirectional EV Charging and Trip Assignment

The integration of bidirectional (V2G) charging allows electric vehicle (EV) fleets to operate as distributed energy assets. However, the joint optimization of charging schedules and trip assignments is NP-hard. Moreover, bidirectional power flows create non-monotonic state-of-charge (SoC) dynamics that weaken standard dual-based Benders cuts. We propose a hybrid quantum-classical Benders decomposition framework. To overcome the qubit overhead associated with encoding feasibility cuts, we introduce logic-based conflict cuts, which require near-zero auxiliary qubits. Furthermore, we develop a sparse recursive SoC formulation that reduces the constraint-matrix density by a factor of T/3 in the horizon length T. We demonstrate that our framework recovers MILP-optimal solutions on benchmark instances with a low auxiliary-qubit budget, and, as a minimal proof of concept, we execute a small instance end-to-end on IBM quantum hardware.