The reduction of CO2 emissions is one of the major challenges in the current century. A game-changer might be quantum computing due to the proposed capabilities. A key field of interest for reducing CO2 emissions is the energy sector being transformed from fossil-based to be based on renewable energies and simultaneously combining electricity, heating, mobility, and manufacturing industries. Here, we study an use case for optimal charging scheduling of battery-electric service vehicles considering the requirements of their tasks, local solar power generation, and their battery capabilities to minimize power grid usage and so CO2 emissions from fossil-based electricity generation. The study compares benchmark results obtained classically with results obtained by the quantum approximate optimization algorithm (QAOA) to show the current capability of gate-based quantum optimization for a real-world use case. We present different formulations of the optimization problem and specific considerations for our use case necessary to yield optimal solutions reproducible with IBM's gate-based quantum computers. Here, we used Qiskit's built-in QAOA method but also self-made methods to examine the influence of the complexity of the problem formulation (penalty factors, landscape of cost function, etc.) as well as the dependence on parameters of the QAOA method (classical optimizer, result extraction, etc.). To obtain reliable results, we used different physical backends and simulations. Finally, we summarize or results and address future improvements for the used QAOA approach for automated real-world applications.
