The logistical management of urban hydrogen fuel cell electric bus (FCEB) fleets presents a computationally complex scheduling problem, especially under dynamic conditions. This paper compares a classical global Mixed-Integer Linear Programming (MILP) baseline with a sequential hybrid quantum–classical model for real-time decision-making (and includes a monolithic quantum comparator for completeness). The hybrid approach employs a classical director to maintain fleet state and, hour by hour, formulates a Quadratic Unconstrained Binary Optimization (QUBO) over candidate actions that is mapped to Ising and solved via the Quantum Approximate Optimization Algorithm (QAOA); the MILP decision is replaced only if the QAOA proposal is feasible and value-improving. Simulation results on a 24-hour, 5-vehicle scenario show that while MILP finds a globally consistent plan, the hybrid method captures short-term opportunities through windowed variational refinement, yielding higher total value; the monolithic quantum solution remains competitive but does not surpass the classical baseline at this scale. The advantage of the hybrid model thus arises from locality and adaptive refinement rather than a Grover-type $\sqrt{N}$ bound, offering a pragmatic path to dynamic fleet management under realistic SOC and capacity constraints.
The logistical management of urban hydrogen fuel cell electric bus (FCEB) fleets presents a computationally complex scheduling problem, especially under dynamic conditions. This paper compares a classical global Mixed-Integer Linear Programming (MILP) baseline with a sequential hybrid quantum–classical model for real-time decision-making (and includes a monolithic quantum comparator for completeness). The hybrid approach employs a classical director to maintain fleet state and, hour by hour, formulates a Quadratic Unconstrained Binary Optimization (QUBO) over candidate actions that is mapped to Ising and solved via the Quantum Approximate Optimization Algorithm (QAOA); the MILP decision is replaced only if the QAOA proposal is feasible and value-improving. Simulation results on a 24-hour, 5-vehicle scenario show that while MILP finds a globally consistent plan, the hybrid method captures short-term opportunities through windowed variational refinement, yielding higher total value; the monolithic quantum solution remains competitive but does not surpass the classical baseline at this scale. The advantage of the hybrid model thus arises from locality and adaptive refinement rather than a Grover-type N bound, offering a pragmatic path to dynamic fleet management under realistic SOC and capacity constraints.
The optimization of front-end crude oil scheduling is a critical determinant of refinery profitability and operational stability. However, the coupling of discrete logistics events (e.g., vessel berthing) with continuous material flows (e.g., pipeline transfers) renders this problem an NP-hard Mixed-Integer Linear Programming (MILP) challenge, often intractable for classical solvers at industrial scales. This study proposes a novel hybrid quantum-classical framework to address these computational bottlenecks. We employ Benders Decomposition to decouple the monolithic model into a discrete Master Problem (MP) and a continuous Subproblem (SP). To exploit the search capabilities of quantum computing, the MP is reformulated as a Quadratic Unconstrained Binary Optimization (QUBO) model and solved via a hybrid quantum solver, while the SP enforces mass balance and quality constraints through iterative optimality and feasibility cuts. Extensive experiments on 15 multi-scale instances demonstrate that the proposed framework significantly outperforms traditional metaheuristics (e.g., Genetic Algorithms, Tabu Search), reducing total operating costs by approximately 73--80% and achieving computational speeds comparable to state-of-the-art commercial solvers (Gurobi). By effectively leveraging global optimality cuts, the method overcomes the tendency of heuristic approaches to trap in local optima, providing a robust and scalable solution for complex refinery logistics.
• We propose a new hybrid quantum-classical algorithm for solving the UC problem. • The hybrid model successfully optimizes 24-hour UC systems from 10 to 1000 units. • The model outperforms classical metaheuristics (GA and SA) and classical MINLP. • This represents an improvement over previous QCUC methods, a step to real-world use. Resource scheduling is critical in many industries, especially in power systems where the Unit Commitment (UC) problem determines the on/off status and output levels of generators under physical and economic constraints. Traditional exact methods, such as Branch‑and‑Bound, Branch‑and‑Cut, dynamic programming and mixed‑integer linear programming (MILP), remain the backbone of UC solution techniques, but they often rely on linear approximations or exhaustive search, leading to high computational burdens as system size grows. Metaheuristic approaches, such as genetic algorithms, particle swarm optimization, and other evolutionary methods, have been explored to mitigate this complexity; however, they typically lack optimality guarantees, exhibit sensitivity to initial conditions, and can become prohibitively time‑consuming for large‑scale systems. In this paper, we introduce a quantum‑classical hybrid algorithm for UC, and other resource scheduling problems by extension, that leverages Benders decomposition to decouple binary commitment decisions from continuous economic dispatch. The binary “master problem” is formulated as a quadratic unconstrained binary optimization (QUBO) model and solved on a quantum annealer. The continuous “subproblem,” which minimizes generation costs, with Lagrangian cuts feeding back to the master until convergence. We evaluate our hybrid framework on systems scaled from 10 to 1,000 generation units. Compared against a classical mixed‑integer nonlinear programming (MINLP) baseline, the hybrid algorithm achieves a consistently lower computation‑time growth rate and maintains an absolute optimality gap below 1.63%. These results demonstrate that integrating quantum annealing within a hybrid quantum-classical Benders decomposition loop can significantly accelerate large‑scale resource scheduling without sacrificing solution quality, pointing toward a viable path for addressing the escalating complexity of modern power grids.
Abstract: Global logistics networks, intercontinental air-freight consolidators, and maritime energy fleets continuously solve large-scale Mixed-Integer Linear Programs (MILPs) such as the Capacitated Vehicle Routing Problem with Time Windows (CVRPTW) and multi-vessel Maritime Inventory Routing Problems (MIRP). When weather disruptions, port congestion, or geopolitical airspace closures invalidate baseline schedules, classical branch-and-cut solvers (Gurobi, CPLEX) experience exponential worst-case tree growth on subproblems exceeding 2,000 binary decision variables, often failing to converge within strict 5-to-15-minute operational re-dispatch windows. Conversely, current Noisy Intermediate-Scale Quantum (NISQ) processors remain limited to 100-to-1,000 physical qubits with finite two-qubit gate fidelity (99.2%−99.8%), preventing direct encoding of full enterprise logistics instances. This paper presents a production-grade Quantum-Classical Hybrid Cloud Architecture that bridges enterprise Kubernetes clusters with co-located quantum processing units (QPUs) via AWS Braket Hybrid Jobs and IBM Quantum Qiskit Runtime primitives. Our framework applies Benders and Dantzig-Wolfe column generation on classical cloud HPC nodes to decompose a 25,000-variable global fleet MILP into a continuous master problem and hard combinatorial pricing/routing subproblems of 60 to 140 binary variables. These subproblems are transformed into Quadratic Unconstrained Binary Optimization (QUBO) and Ising Hamiltonians, warm-started from classical linear programming (LP) relaxations (WS-QAOA), compiled with dynamical decoupling and Zero-Noise Extrapolation (ZNE), and executed inside co-located QPU-CPU sessions while a GPU-accelerated Simulated Bifurcation (SB) digital annealer runs in parallel as a deterministic SLA fallback. Evaluated on disruption recovery workloads modeled on ExxonMobil maritime LNG routing and DHL Global Forwarding air-cargo container loading, our hybrid WS-QAOA + Column Generation workflow improves optimality gap closure at a 10-minute SLA cutoff from 6.84% (classical branch-and-bound alone) to 1.42%, reduces emergency re-routing compute wall-clock time by 61.5%, and cuts fleet fuel and charter penalty costs by 4.7%. Research Domain & Specialization Track Master of Science in Information Technology (MSIT) — Quantum Cloud Computing, Hybrid Orchestration, and Operations Research. Core Technical Highlights Empirical Production Case Studies: Rigorous architectural blueprints and telemetry evaluation across enterprise cloud deployments. Four-Tier Reference Architecture: Formal specification from edge ingress to distributed hardware execution pools. Mathematical Formulation: Formally derived algorithmic and optimization models with closed-loop verification. Multi-Modal Benchmarking: Comparative empirical baselines under fault-injection and synthetic workload scaling. Author Information Author: Sonu Kumar SinghRole: Senior Consultant Affiliation: Independent Researcher Publication Status: Preprint / Working Paper (MSIT AI & Cloud Systems Research Series) Reproducibility & Open Science All included architecture diagrams, telemetry schemas, and benchmark curves are open-access under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.
We suggest a hybrid quantum-classical routine for the NP-hard Electric Vehicle Fleet Charging and Allocation Problem. The original formulation is a Mixed Integer Linear Program with continuous variables and inequality constraints. To separate inequality constraints that are difficult for quantum routines we use a decomposition in master and pricing problems: the former targets the assignment of vehicles to reservations and the latter suggests vehicle exploitation plans that respect the battery state-of-charge constraints. The master problem is equivalent to the search for an optimal set partition. In our hybrid scheme, the master problem is reformulated in a quadratic unconstrained binary optimization problem which can be solved with quantum annealing on the DWave Advantage system. On large instances, we benchmark the performance of the decomposition technique with classical and quantum-inspired metaheuristics: simulated annealing, tabu search, and vector annealing by NEC. The numerical results with purely classical solvers are comparable to the solutions from the traditional mixed integer linear programming approaches in terms of solution quality while being faster. In addition, it scales better to larger instances. The major advantage of the proposed approach is that it enables quantum-based methods for this realistic problem with many inequality constraints. We show this by initial studies on DWave hardware where optimal solutions can be found for small instances.
Drone-delivery planning combines routing decisions with operational constraints such as payload capacity and limited onboard energy, resulting in combinatorial optimization problems that can become costly to encode directly in binary form. This work investigates a hybrid quantum--classical approach in which candidate drone missions are generated and evaluated classically before constructing a quadratic unconstrained binary optimization (QUBO) model for mission selection. Payload- and energy-infeasible missions are removed during preprocessing, while the reduced QUBO is solved using exact enumeration, simulated annealing (SA), and the Quantum Approximate Optimization Algorithm (QAOA), with mixed-integer linear programming (MILP) used as a classical reference. Experiments on controlled synthetic delivery instances evaluate solution quality, the effect of preprocessing, and computational scaling. Exact QUBO optimization reproduces the MILP optimum on the evaluated small instances, while SA achieves 100% feasibility with a median optimality gap of 0%. Combined payload-and-energy preprocessing reduces the mean number of QUBO variables by 29.60% and quadratic interactions by 49.20%, while reducing mean SA runtime by 31.26%. In contrast, the evaluated shallow statevector-based QAOA configuration achieves lower feasibility and is restricted to small QUBO instances. These results indicate that, in the considered setting, the main practical benefit of the hybrid architecture comes from classical feasibility preprocessing that reduces the binary search space before QUBO-based optimization.
We present a quantum optimization framework for the Shipment Selection Problem (SSP) in electric freight logistics, developed jointly by IonQ and Einride. Idle gaps arising from stochastic shipment cancellations reduce fleet utilization and revenue; filling them optimally requires solving a combinatorial assignment problem with quadratic inter-gap dependencies. We formulate the SSP as a Mixed-Integer Quadratic Program, map it to an Ising cost Hamiltonian, and solve it using Iterative-QAOA, a non-variational warm-start extension of the Quantum Approximate Optimization Algorithm (QAOA) with a fixed linear-ramp parameter schedule. An end-to-end hybrid workflow integrates Einride's vehicle routing problem (VRP) solver with IonQ's quantum simulations, enabling evaluation on real, anonymized logistics data spanning up to 130 qubits. We assess solution quality through application-level performance metrics, including Shipments Delivered (SD), Schedule Compatibility Score (SCS), and Total Drive Distance (TDD). When the quantum assignment is passed to the classical solver as a warm start, the resulting hybrid workflow achieves improvements of up to 12% in SD and a reduction of up to 6% in total drive distance per shipment for specific instances, while total operational cost remains effectively unchanged. For the subset of instances within reach of current devices (20-35 qubits), the workflow is additionally executed on IonQ trapped-ion quantum hardware, where the hardware results closely reproduce the noiseless simulations. These results show that Iterative-QAOA can generate compatibility-aware assignments that become operationally valuable when embedded in a hybrid logistics optimization workflow.