Siting a limited number of fast-charging hubs so that the greatest share of urban charging demand falls within reach is a discrete, NP-hard facility-location task that grows combinatorially with the number of candidate parcels. We recast this task for gate-model quantum hardware. Demand intensity and candidate parcels are extracted from a public Government of NCT of Delhi charging-station record of 2,270 georeferenced points, a demand-weighted maximumcoverage objective with a cardinality constraint is mapped to a Quadratic Unconstrained Binary Optimization (QUBO) model, and the QUBO is expressed as an Ising cost Hamiltonian solved by the Quantum Approximate Optimization Algorithm (QAOA). On a twelve-parcel instance selecting five hubs, exact enumeration places the optimum at 53.2% covered demand; QAOA recovers an approximation ratio that rises from 0.67 at depth p=1 to 0.93 at p=3, while a depth-four circuit regresses to 0.83 under a fixed optimizer budget, illustrating the trainability cost of added layers. At this NISQ-tractable size, greedy and simulated-annealing baselines both reach the exact optimum, so the quantum contribution is algorithmic rather than a wall-clock advantage; an explicit size sweep shows the classical search space and exact-solve effort growing as 2^N, which is where deeper quantum circuits are expected to matter. The study is reported transparently, including the negative parity results.
Siting a limited number of fast-charging hubs so that the greatest share of urban charging demand falls within reach is a discrete, NP-hard facility-location task that grows combinatorially with the number of candidate parcels. We recast this task for gate-model quantum hardware. Demand intensity and candidate parcels are extracted from a public Government of NCT of Delhi charging-station record of 2,270 georeferenced points, a demand-weighted maximumcoverage objective with a cardinality constraint is mapped to a Quadratic Unconstrained Binary Optimization (QUBO) model, and the QUBO is expressed as an Ising cost Hamiltonian solved by the Quantum Approximate Optimization Algorithm (QAOA). On a twelve-parcel instance selecting five hubs, exact enumeration places the optimum at 53.2% covered demand; QAOA recovers an approximation ratio that rises from 0.67 at depth p=1 to 0.93 at p=3, while a depth-four circuit regresses to 0.83 under a fixed optimizer budget, illustrating the trainability cost of added layers. At this NISQ-tractable size, greedy and simulated-annealing baselines both reach the exact optimum, so the quantum contribution is algorithmic rather than a wall-clock advantage; an explicit size sweep shows the classical search space and exact-solve effort growing as 2^N, which is where deeper quantum circuits are expected to matter. The study is reported transparently, including the negative parity results.
Optimal routing problems of electric vehicles (EVs) have attracted much attention in recent years, and installation of charging stations is an important issue for EVs. Hence, we focus on the joint optimization of the location of charging stations and the routing of EVs. When routing problems are formulated in the form of quadratic unconstrained binary optimization (QUBO), specialized solvers such as quantum annealers are expected to provide optimal solutions with high speed and accuracy. However, battery capacity constraints make it hard to formulate into QUBO form without a large number of auxiliary qubits. Here, we propose a sequential optimization method utilizing the Bayesian inference and QUBO solvers, in which the battery capacity constraints are automatically learned. This method enables us to optimize the number and location of charging stations and the routing of EVs with a small number of searches. Applying this method to a routing problem of 20 locations, we observed consistent convergence toward battery-feasible solutions across independent runs, demonstrating stable learning behavior of the proposed framework. Small-scale validation experiments using exhaustive enumeration show that the framework reliably discovers feasible configurations close to the global optimum, while runtime and QUBO-size analyses clarify its computational characteristics.
The rapid deployment of electric vehicles (EVs) in public parking facilities and fleet operations raises challenging intra-day charging scheduling problems under tight charger capacity and limited dwell times. We model this problem as a variant of the Partition Coloring Problem (PCP), where each vehicle defines a partition, its candidate charging intervals are vertices, and temporal and resource conflicts are represented as edges in a conflict graph. On this basis, we design a branch-and-price algorithm in which the restricted master problem selects feasible combinations of intervals, and the pricing subproblem is a maximum independent set problem. The latter is reformulated as a quadratic unconstrained binary optimization (QUBO) model and solved by quantum-annealing-inspired algorithms (QAIA) implemented in the MindQuantum framework, specifically the ballistic simulated branching (BSB) and simulated coherent Ising machine (SimCIM) methods, while the master problem is solved by Gurobi. Computational experiments on a family of synthetic EV charging instances show that the QAIA-enhanced algorithms match the pure Gurobi-based branch-and-price baseline on small and medium instances, and clearly outperform it on large and hard instances. In several cases where the baseline reaches the time limit with non-zero optimality gaps, the QAIA-based variants close the gap and prove optimality within the same time budget. These results indicate that integrating QAIA into classical decomposition schemes are a promising direction for large-scale EV charging scheduling and related PCP applications.
It is imperative to reduce carbon dioxide emissions and fossil fuel consumption to ensure the Earth's sustainable future and mitigate negative impacts like extreme climate changes caused by greenhouse gases. Electric vehicles (EVs) play a pivotal role in this context, where the convenience of charging stations is crucial in influencing consumer choices. This paper formulates the placement of charging stations as an optimization problem, considering factors like station density, accessibility, coverage, and regional cost variations, to minimize total construction costs. The problem is mapped onto a quadratic unconstrained binary optimization (QUBO) model. The QUBO can efficiently represent and solve complex combinatorial optimization problems, making it suitable for quantum and advanced classical algorithms. Utilizing digital quantum annealing, the optimal or near-optimal solutions are efficiently identified. The performance of the proposed approach is compared with classical algorithms, including mixed linear programming and simulated annealing, demonstrating significant advancements of digital annealing.
Real-time control of a compact spherical-tokamak breeder poses, at several points, a combinatorial-optimization problem inside a control cycle: which actuators to schedule, how to lay out a discrete blanket, and — the control-relevant case — how to sequence poloidal- and toroidal-field coil currents under hard constraints while tracking a shape and vertical-position target. Because these problems are naturally binary and quadratic, they are the canonical near-term target for quantum optimization, and it is a fair, testable question whether a quantum processor solves them faster or better than a classical one. This paper answers that question with a formal treatment and a pre-registered result. We derive compact quadratic-unconstrained-binary-optimization (QUBO) encodings for all three problems from first principles — pulse cadence as a number-partitioning Ising model, blanket layout as a penalty-embedded assignment, and coil-current/actuator scheduling as a fixed-point-encoded quadratic tracking objective built on the free-boundary equilibrium shape-response Jacobian — and map each to two fault-tolerant primitives, a depth-three quantum approximate optimization ansatz (QAOA, p=3) and a D\"urr–Hyer Grover minimum-finder. At the frozen breeder design point (I_p=9.66 MA, Q=3.076, P_fus=85.04 MW, negative triangularity δ=-0.30, B_0=8 T, κ=2.0, =1.20 m, aspect ratio A=2.5, centrepost peak field 16.84 T) the design-scale instances need 23–61 logical qubits and 5×10^3–5.5×10^7 T-gates, verified against the Fowler surface-code and D\"urr–Hyer formulas across 50 resource rows with zero discrepancies. On the question of whether quantum hardware helps, we report an explicit negative: classical simulated annealing matches or beats QAOA on all three breeder QUBOs out to n=120 variables; the exact-to-heuristic crossover sits at n=12–16 (exact optima in 0.03–292 s of wall time); the QAOA approximation ratio plateaus at 0.90–0.95 and the circuits become classically unverifiable past n≈24; and a fleet-scale (n=120) Grover formulation would need 1.8×10^18 oracle calls and 1.2×10^23 T-gates — a resource boundary, not a route. We therefore place variational quantum reinforcement learning for shape and vertical-position control on a dated, benchmark-gated schedule: a quantum policy is admitted only if it meets or beats the classical controller at equal wall-clock with a control-barrier-certified safety filter held inviolate. All quantum and classical runs were carried out on the NVIDIA GPU HPC campaign. The deliverable is the honest, resource-grounded map of where quantum computing does — and does not — pay for real-time fusion control. Key results (frozen anchors): N_T = 1.2 ×10^23. Methods & codes: FreeGSNKE, FreeGS, Sauter, QAOA, VQE, ADAPT-VQE. Live verification: 4 gate validator(s) with live-recompute cards (2 reproduced, 1 revised, 1 estimated). See the Verification section and data/verification.csv. Related: Paper page · De-risking register · 3D model · Learn more about Kronos Part of the 2026 Kronos publication series; independently re-run and stamped in the Kronos de-risking register (DOI 10.5281/zenodo.22645689). All numerical values are frozen design-point anchors; see the register. Public research artifact. No proprietary, financial, or supply-chain information is included.
The Capacitated Vehicle Routing Problem (CVRP) is a combinatorial optimization problem that can be formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, making it a potential application for near-term quantum optimization. This paper benchmarks the Quantum Approximate Optimization Algorithm (QAOA, p = 2) against Google OR-Tools Guided Local Search on a seeded instance with three customers and two vehicles. The study examines the QUBO formulation, energy spectrum, optimization behavior, penalty weights, Hamiltonian scaling, and circuit depths. The experiments show that the tested QAOA configurations do not reliably concentrate probability on optimal solutions. The classical solver identifies the optimal solution for the selected instance. The study provides a reproducible baseline and discusses limitations and future research directions. The findings are limited to the tested instance, formulation, and optimization configurations.
The Traveling Salesman Problem (TSP) is a fundamental challenge in combinatorial optimization, widely applied in logistics and transportation. As the size of TSP instances grows, traditional algorithms often struggle to produce high-quality solutions within reasonable timeframes. This study investigates the potential of the Quantum Approximate Optimization Algorithm (QAOA), a hybrid quantum-classical method, to solve TSP under realistic constraints. We adopt a QUBO-based formulation of TSP that integrates real-world logistical constraints reflecting operational conditions, such as vehicle capacity, road accessibility, and time windows, while ensuring compatibility with the limitations of current quantum hardware. Our experiments are conducted in a simulated environment using high-performance computing (HPC) resources to assess QAOA's performance across different problem sizes and quantum circuit depths. In order to improve scalability, we propose clustering QAOA (Cl-QAOA), a hybrid approach combining classical machine learning with QAOA. This method decomposes large TSP instances into smaller sub-problems, making quantum optimization feasible even on devices with a limited number of qubits. The results offer a comprehensive evaluation of QAOA's strengths and limitations in solving constrained TSP scenarios. This study advances quantum optimization and lays groundwork for future large-scale applications.