A frequent starting point of quantum computation platforms are two-state quantum systems, i.e., qubits. However, in the context of integer optimization problems, relevant to scheduling optimization and operations research, it is often more resource-efficient to employ quantum systems with more than two basis states, so-called qudits. Here, we discuss the quantum approximate optimization algorithm (QAOA) for qudit systems. We illustrate how the QAOA can be used to formulate a variety of integer optimization problems such as graph coloring problems or electric vehicle (EV) charging optimization. In addition, we comment on the implementation of constraints and describe three methods to include these into a quantum circuit of a QAOA by penalty contributions to the cost Hamiltonian, conditional gates using ancilla qubits, and a dynamical decoupling strategy. Finally, as a showcase of qudit-based QAOA, we present numerical results for a charging optimization problem mapped onto a max-k-graph coloring problem. Our work illustrates the flexibility of qudit systems to solve integer optimization problems.

The reduction of CO 2 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 CO 2 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 CO 2 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.

Battery electric service vehicles are one step to reduce CO 2 emissions in the mobility sector. We present an use case for optimal charging scheduling in combination with local solar power generation to minimize power grid usage. The study compares results obtained with a classical optimizer and with a quantum computing algorithm on real quantum hardware. It is shown that for most benchmark experiments, the quantum computing method yields an optimal solution however the quantum approximate optimization algorithm is more sensitive to penalty factors than the classical optimization. Additionally, we present a comparison of the computing times and give a brief review of the current state of IBM’s gate-based quantum computing.