Large-scale combinatorial optimization remains demanding for classical heuristics, particularly when dense Quadratic Unconstrained Binary Optimization (QUBO) formulations induce large memory footprints, high CPU utilization, and long execution times. While near-term quantum processors cannot yet deliver unconditional quantum advantage, hybrid architectures can provide practical value by reducing the resource burden. This paper presents a resource-efficiency study of Hybrid Quantum Neighborhood Selection (HQNS), a framework that decomposes large dense QUBO instances into bounded-width quantum subproblems via stochastic frontier selection. We evaluate HQNS on the Maximum Diversity Subset Selection Problem (MDSSP), focusing on the trade-off between solution quality retention and resource consumption. Benchmarks up to N=1000 candidates show that HQNS preserves 99.9908% of the mean diversity score of an 11-restart parallel Simulated Annealing baseline, while reducing wall-clock time by 94.91%, peak CPU utilization by 64.68%, and peak memory usage by 88.61%. The QPU execution time remains bounded within a 6-7 second envelope across scales, indicating that the quantum component is decoupled from the global QUBO dimension when the frontier size is fixed. These results suggest that HQNS provides a resource-aware pathway for deploying hybrid quantum optimization in practical large-scale settings, serving as an efficient architecture for incorporating near-term quantum processors into classical optimization pipelines.
Large-scale combinatorial optimization remains demanding for classical heuristics, particularly when dense Quadratic Unconstrained Binary Optimization (QUBO) formulations induce large memory footprints, high CPU utilization, and long execution times. While near-term quantum processors cannot yet deliver unconditional quantum advantage, hybrid architectures can provide practical value by reducing the resource burden. This paper presents a resource-efficiency study of Hybrid Quantum Neighborhood Selection (HQNS), a framework that decomposes large dense QUBO instances into bounded-width quantum subproblems via stochastic frontier selection. We evaluate HQNS on the Maximum Diversity Subset Selection Problem (MDSSP), focusing on the trade-off between solution quality retention and resource consumption. Benchmarks up to N=1000 candidates show that HQNS preserves 99.9908% of the mean diversity score of an 11-restart parallel Simulated Annealing baseline, while reducing wall-clock time by 94.91%, peak CPU utilization by 64.68%, and peak memory usage by 88.61%. The QPU execution time remains bounded within a 6-7 second envelope across scales, indicating that the quantum component is decoupled from the global QUBO dimension when the frontier size is fixed. These results suggest that HQNS provides a resource-aware pathway for deploying hybrid quantum optimization in practical large-scale settings, serving as an efficient architecture for incorporating near-term quantum processors into classical optimization pipelines.
Large-scale combinatorial optimization is a challenge for near-term quantum computing because dense Quadratic Unconstrained Binary Optimization (QUBO) formulations yield interaction graphs that exceed the limits of NISQ processors. This work introduces Hybrid Quantum Neighborhood Selection (HQNS), a hybrid framework mitigating this via stochastic frontier decomposition. Instead of encoding all N variables into a monolithic circuit, HQNS selects a compact frontier of F << N active variables per stage, freezing the rest into reduced QUBO coefficients. A multi-stage crawling procedure rotates these frontiers, letting local quantum subproblems refine a global solution. We evaluate HQNS on the Maximum Diversity Subset Selection Problem (MDSSP) across six scales, N up to 1000. Circuit burden is reduced from the dense QAOA requirement of O(N^2) two-qubit terms per layer to O(F^2) per stage, with total complexity governed by the number of stages and classical overhead. Benchmarks show that HQNS achieves competitive solution quality relative to parallel simulated annealing (SA) while maintaining bounded circuit width and stable QPU time. In the N=1000 benchmark over ten executions, HQNS preserves 99.9908% of the mean diversity score of an 11-restart parallel SA baseline, while reducing wall-clock time by 65.03%, peak CPU usage by 55.97%, and peak memory by 35.21%. Ablation shows performance depends on frontier size, warm-starts, CVaR filtering, and stochastic rotation. These results demonstrate that structured frontier decomposition makes variational optimization executable for dense QUBO instances unsuitable for direct QAOA on present hardware.
Over the past decades, the operations research community has developed numerous effective optimization algorithms, yet quantum computing is emerging as a new computational paradigm with the potential to approach optimization problems more efficiently. Grover's algorithm offers a provable speedup for combinatorial optimization, but its circuit depth places it beyond current noisy intermediate-scale quantum (NISQ) devices. A more accessible alternative is to reformulate the optimization problem as a quadratic unconstrained binary optimization (QUBO) problem and apply quantum annealing; however, practical problem instances remain out of reach for existing hardware. We introduce AtomTreeSearch, a hybrid classical-quantum algorithm that integrates a quantum subroutine natively implementable on neutral-atom quantum computers within a Monte Carlo Tree Search framework. At each expansion step, a maximal weighted independent set of candidate actions provided by the quantum processor is selected, and these collective actions are performed to obtain a child node. We benchmark our method on the Traveling Salesman Problem, with instances of up to 60 cities on random Euclidean instances and up to 100 cities on TSPLIB instances. Our hybrid algorithm generally matches or outperforms both OR-Tools and simulated annealing on these instances, and we find that the quantum subroutine produces more diverse and higher-quality branches compared to classical alternate subroutines. These results suggest that carefully scoped quantum subroutines embedded in classical search frameworks represent a promising path toward near-term quantum utility in combinatorial optimization.
We perform an end-to-end benchmark of a hybrid sequential quantum computing (HSQC) solver for higher-order unconstrained binary optimization (HUBO), executed on IBM Heron r3 quantum processors to evaluate the potential of current quantum hardware for combinatorial optimization with sub-second end-to-end runtimes. All reported runtimes include the complete pipeline--from preprocessing to QPU execution and postprocessing--under strict wall-clock accounting. Across 20 benchmark instances, a single hybrid attempt produces high-quality solutions in less than one second, matching the ground-state energy in 14 cases. At the same runtime, CPU-based solvers, including simulated annealing, memetic tabu search, and EasySolve, do not reach the value obtained by HSQC, whereas an enhanced parallel tempering method and the GPU-accelerated solver ABS3 reach or surpass it. These results show that HSQC, executed on a single QPU, can achieve performance competitive with strong classical solvers running on 128 vCPUs or 8 NVIDIA A100 GPUs, while also providing a reproducible system-level benchmark for tracking progress as quantum hardware and hybrid sequential workflows improve.
As quantum computing advances, quantum approximate optimization algorithms (QAOA) have shown promise in addressing combinatorial optimization problems. However, the limitations of Noisy Intermediate Scale Quantum (NISQ) devices hinder the scalability of QAOA for large-scale optimization tasks. To overcome these challenges, we propose Backbone-Driven QAOA, a hybrid framework that leverages adaptive Tabu search for classical preprocessing to decompose large-scale quadratic unconstrained binary (QUBO) problems into NISQ-compatible subproblems. In our approach, adaptive Tabu search dynamically identifies and fixes backbone variables to construct reduced-dimensional subspaces that preserve the critical optimization landscape. These quantum-tractable subproblems are then solved via QAOA, with the resulting solutions iteratively refining the backbone selection in a closed-loop quantum-classical cycle. Experimental results demonstrate that our approach not only competes with, and in some cases surpasses, traditional classical algorithms but also performs comparably with recently proposed hybrid classical-quantum algorithms. Our proposed framework effectively orchestrates the allocation of quantum and classical resources, thereby enabling the solution of large-scale combinatorial optimization problems on current NISQ hardware.
Near-term quantum optimizers accommodate roughly a hundred binary variables, requiring large Quadratic Unconstrained Binary Optimization problems to be decomposed into hardware-sized subproblems while other variables remain fixed. Variables are typically selected by ranking the objective changes from individual flips. We show that this rule is uninformative once the incumbent is optimal under single-variable flips: every score represents a cost, while remaining improvements depend on overlooked pairwise interactions. A second-order expansion instead yields a prize-collecting densest-subgraph selection problem, solvable greedily in time linear in the number of variables, and two solver-free bounds bracketing the improvement achievable within a selected subset. On transportation networks from Chicago and Philadelphia, our rule with 16-variable subproblems outperforms random selection with 64, demonstrating that quadrupling device capacity cannot compensate for weaker selection. Replacing geometric adjacency with road-network connectivity widens the margin by a factor of 1.6-1.9. With the selection trace fixed, varying the fraction of subproblems solved on a 120-qubit device from zero to one leaves the final objective unchanged to six significant figures. At tested hardware-accessible sizes, gains therefore arise from selection rather than the backend. Hardware feasibility is limited by coupling terms: 120-variable problems fail to compile with 7,260 terms but succeed with 5,118. Compilation scales almost quadratically with term count and dominates execution cost, reaching 1,752 seconds versus 469 seconds of quantum processing.
Quantum computing promises computational advantages for solving complex optimization problems; however, current Noisy Intermediate-Scale Quantum (NISQ) devices suffer from limited qubit counts, short coherence times, and high error rates. Fully fault-tolerant quantum algorithms remain impractical in the near term, necessitating hybrid approaches that integrate classical and quantum computation. This paper proposes a Hybrid Quantum–Classical Machine Learning Framework (HQC-MLF) for large-scale combinatorial and continuous optimization tasks. The framework leverages parameterized quantum circuits (PQCs) embedded within classical optimization loops, enabling efficient search in high-dimensional spaces while mitigating hardware constraints. We introduce adaptive ansatz selection, classical preconditioning, error mitigation strategies, and resource-aware scheduling to enhance scalability. Experimental evaluations on logistics routing, portfolio optimization, and energy load balancing demonstrate improved convergence speed and solution quality compared to purely classical baselines under realistic NISQ simulations. The proposed architecture provides a practical pathway toward near-term quantum advantage in real-world optimization problems