Variational quantum algorithms have attracted attention for their potential to solve combinatorial optimization problems. We study how the choice of encoding affects the resource requirements and optimization behavior of a variational quantum optimization algorithm. In order to quantify these effects, realistically inspired constrained electric vehicle (EV) fleet management problems were considered. These problems couple determining the optimal EV battery charging schedule with assigning EVs to trips requested by customers. We compare a conventional binary (qubit) trip encoding with an integer (qudit) encoding that represents assignments more directly. Both encodings guarantee the same feasible solution set, while the qudit encoding exponentially reduces the required Hilbert-space dimension. We solve many random instances of highly constrained uni- and bi-directional charging problems using qudit-based quantum approximate optimization algorithm (QAOA) and thoroughly evaluate the performance results. We find that the qudit encoding of customer trips achieves similar or better optimization performance at much reduced resource requirements and shorter simulation runtime. These results highlight qudit-native encodings as a practical route for integer and multi-valued scheduling problems in variational quantum optimization.
Variational quantum algorithms have attracted attention for their potential to solve combinatorial optimization problems. We study how the choice of encoding affects the resource requirements and optimization behavior of a variational quantum optimization algorithm. In order to quantify these effects, realistically inspired constrained electric vehicle (EV) fleet management problems were considered. These problems couple determining the optimal EV battery charging schedule with assigning EVs to trips requested by customers. We compare a conventional binary (qubit) trip encoding with an integer (qudit) encoding that represents assignments more directly. Both encodings guarantee the same feasible solution set, while the qudit encoding exponentially reduces the required Hilbert-space dimension. We solve many random instances of highly constrained uni- and bi-directional charging problems using qudit-based quantum approximate optimization algorithm (QAOA) and thoroughly evaluate the performance results. We find that the qudit encoding of customer trips achieves similar or better optimization performance at much reduced resource requirements and shorter simulation runtime. These results highlight qudit-native encodings as a practical route for integer and multi-valued scheduling problems in variational quantum optimization.
Variational quantum algorithms have attracted attention for their potential to solve combinatorial optimization problems. We study how the choice of encoding affects the resource requirements and optimization behavior of a variational quantum optimization algorithm. In order to quantify these effects, realistically inspired constrained electric vehicle (EV) fleet management problems were considered. These problems couple determining the optimal EV battery charging schedule with assigning EVs to trips requested by customers. We compare a conventional binary (qubit) trip encoding with an integer (qudit) encoding that represents assignments more directly. Both encodings guarantee the same feasible solution set, while the qudit encoding exponentially reduces the required Hilbert-space dimension. We solve many random instances of highly constrained uni- and bi-directional charging problems using qudit-based quantum approximate optimization algorithm (QAOA) and thoroughly evaluate the performance results. We find that the qudit encoding of customer trips achieves similar or better optimization performance at much reduced resource requirements and shorter simulation runtime. These results highlight qudit-native encodings as a practical route for integer and multi-valued scheduling problems in variational quantum optimization.
Complex optimization problems, such as traffic routing and electric vehicle (EV) charging scheduling, are becoming increasingly challenging for intelligent transportation systems (ITSs), in particular as computational resources are limited and network conditions evolve frequently. This paper explores a quantum computing approach to address these issues by proposing a hybrid quantum-classical (HQC) workflow that leverages the variational quantum eigensolver (VQE), an algorithm particularly well suited for execution on noisy intermediate-scale quantum (NISQ) hardware. To this end, the EV charging scheduling and traffic routing problems are both reformulated as binary optimization problems and then encoded into Ising Hamiltonians. Within each VQE iteration, a parametrized quantum circuit (PQC) is prepared and measured on the quantum processor to evaluate the Hamiltonian’s expectation value, while a classical optimizer—such as COBYLA, SPSA, Adam, or RMSProp—updates the circuit parameters until convergence. In order to find optimal or nearly optimal solutions, VQE uses PQCs in combination with classical optimization algorithms to iteratively minimize the problem Hamiltonian. Simulation results exhibit that the VQE-based method increases the efficiency of EV charging coordination and improves route selection performance. These results demonstrate how quantum computing will potentially advance optimization algorithms for next-generation ITSs, representing a practical step toward quantum-assisted mobility solutions.
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.
The vehicle routing problem with time windows (VRPTW) is a common optimization problem faced within the logistics industry. In this work, we explore the use of a previously-introduced qubit encoding scheme to reduce the number of binary variables, to evaluate the effectiveness of NISQ devices when applied to industry relevant optimization problems. We apply a quantum variational approach to a testbed of multiple VRPTW instances ranging from 11 to 3964 routes. These intances were formulated as quadratic unconstrained binary optimization (QUBO) problems based on realistic shipping scenarios. We compare our results with standard binary-to-qubit mappings after executing on simulators as well as various quantum hardware platforms, including IBMQ, AWS (Rigetti), and IonQ. These results are benchmarked against the classical solver, Gurobi. Our approach can find approximate solutions to the VRPTW comparable to those obtained from quantum algorithms using the full encoding, despite the reduction in qubits required. These results suggest that using the encoding scheme to fit larger problem sizes into fewer qubits is a promising step in using NISQ devices to find approximate solutions for industry-based optimization problems, although additional resources are still required to eke out the performance from larger problem sizes.
A frequent starting point of quantum computation platforms is the two-state quantum system, i.e., the qubit. 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 charging optimization. In addition, we comment on the implementation of constraints and describe three methods to include these in 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 maximum-k-graph-coloring problem. Our work illustrates the flexibility of qudit systems to solve integer optimization problems.
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.