Results suggest that near-term quantum sampling is most useful as a selective local repair mechanism rather than as a replacement for classical routing heuristics.
Abstract
This study develops a hybrid quantum-classical framework for constrained vehicle routing problems, focusing on the pickup-and-delivery problem with time windows. Instead of casting the full routing problem as a stand-alone quantum optimization task, we embed shallow quantum samplers inside the repair phase of an Adaptive Large Neighbourhood Search (ALNS) heuristic. A Deep Q-Network controller decides whether each reduced repair subproblem should be handled by a classical repair heuristic or by a quantum sampler, using features that describe the local repair structure and predicted hardware reliability. IBM Heron experiments are used to calibrate an empirical noise-aware model for local quantum repair circuits. Across the tested instances, quantum repair is admissible in only about 16% of reduced repair states and is not superior on average. However, under selected matched repair budgets, quantum-enabled repair reduces the final gap relative to standard ALNS in 29 of 36 tested settings. These results suggest that near-term quantum sampling is most useful as a selective local repair mechanism rather than as a replacement for classical routing heuristics.
The results suggest that quantum kernels may serve as complementary routing-aware decomposition modules within classical optimization pipelines, particularly for offline structural preprocessing.
Quantum optimization has attracted growing interest as quantum hardware continues to improve, yet state-of-the-art classical solvers remain a formidable benchmark for practical utility. Rather than seeking a fully quantum replacement for classical optimization, we propose a hybrid strategy that uses quantum information to enhance leading classical heuristics. Specifically, we introduce a warm-start method based on local correlators obtained from the Quantum Approximate Optimization Algorithm (QAOA), and use this information to initialize the Burer-Monteiro (BM) rank-two relaxation. We demonstrate numerically that, compared to a random, multi-start initialization baseline (a standard strategy used for BM), this quantum-informed initialization offers a significant head start, i.e., high-quality solutions with very small number of iterations, for two problem classes -- random Erd\H{o}s R\'{e}nyi graphs with edge density of $10\%$ (ER-10) and fully-connected Sherrington Kirkpatrick (SK) spin glass models, at $n=500$ and $n=1000$ qubits. At the same time, given enough iterations, the random baseline often eventually catches up and slightly outperforms the warm-start strategy on average, an effect visibly stronger for $n=500$ than for $n=1000$. The results demonstrate an exploitation/exploration tradeoff of using WS to quickly arrive at very good solutions vs exploring slightly better solutions with a larger iterations budget via a standard strategy. Our results highlight how low-depth quantum circuits can provide useful structural information for classical optimization and suggest a promising route toward near-term quantum utility through quantum-assisted initialization.
Bao Gia Bach, Ilya Safro, Filip B. Maciejewski· 0 citations
Current quantum computers do not yet have the required qubit resources to meet the demands of most practical quantum algorithms. To circumvent this constraint, the practice of dividing these algorithms into parts through quantum circuit cutting has been explored. Many of these works either show exponential scaling or are far from optimal solutions. In this paper, MosaiQC is presented as a novel framework to improve upon existing circuit cutting frameworks. A hybrid warmstart with refinement optimization is used to find cutting solutions, allowing the combination of both wire and gate cuts. Additionally, MosaiQC enables hardware partitions of mixed sizes. Furthermore, the refinement stage incorporates a fast approximate quadratic assignment solver to better place hardware partitions, demonstrating a mean local fidelity improvement of $19.56 \% \pm 6.17\%$ over the baseline algorithm. In runtime and sampling overhead costs, improvements of $2.88 \times$ and an average of $16.84\%$ cut reduction (resulting in an average $5.83 \cdot 10^{11} \times$ overhead reduction) are observed. MosaiQC demonstrates a superior trade-off for run speed and solution quality, while adding fundamental features excluded by most competitors. With this, MosaiQC demonstrates that scalable heuristic optimization can substantially reduce the computational overhead of circuit-cut placement for increasingly large quantum circuits.
Koen J. Mesman, Yinglu Tang, Matthias Moller et al.· 0 citations
The Maximal Covering Location Problem (MCLP) is an NP-hard Combinatorial Optimization Problem (COP) that aims to determine the optimal facility placements that maximize total coverage. It is characterized by both equality and inequality constraints, which ensure correct coverage but significantly increase the complexity of exploring the solution space as instance size grows. Hybrid quantum-classical approaches might offer a promising alternative to classical optimization methods by enabling the exploration of complex energy landscapes through quantum superposition and probabilistic sampling. In this work, the MCLP is formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model, where constraint embedding plays a critical role in solution quality. In particular, Unbalanced Penalization (UP) is employed as an alternative to the Slack Variables (SV) for handling inequality constraints without increasing the number of variables. This study focuses on QAOA and one of its variants, the WS-QAOA, which leverages a biased initial state derived from a continuous relaxation of the problem. Additionally, a linear ramp (LR) parameter schedule is incorporated to reduce optimization complexity. The performance of these techniques is evaluated both individually and in combination, as a function of circuit depth $p$ and problem size. Results show that the combined approach of UP, LR, and WS-QAOA consistently improves solution quality and feasibility metrics, while maintaining robust performance as the problem size increases, highlighting its potential within hybrid quantum-classical optimization frameworks.
Jorge Saavedra-Benavides, J. A. Montañez-Barrera, Alberto Maldonado-Romo et al.· 0 citations
This paper presents a comprehensive investigation of quantum annealing and hybrid quantum-classical algorithms applied to unit load device (ULD) configuration and disruption management in air cargo and multimodal logistics networks, and provides a practical roadmap for near-term adoption of quantum technologies in high-stakes logistics environments.
V. Sharma· International Journal of Cre...· 0 citations
We investigate and compare the performance of two quantum optimization approaches, the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing, applied to the Minimum Vertex Cover (MVC) problem. The problem is encoded as an and Ising model, and experiments are conducted on IBM’s GenericBackendV2 noisy superconducting qubit simulator and the D-Wave Advantage2 quantum annealer. Performance is evaluated in terms of solution quality, measurement probability, and proportion of valid solutions. The results we obtained show that, within our experimental setting, quantum annealing consistently outperforms its classical counterpart on small instances, while QAOA, though currently limited by simulation constraints, shows promising behavior that improves with increasing circuit depth. As problem size grows, both approaches exhibit sensitivity to parameter choices such as the penalty term and graph density, underscoring the need for careful tuning. These findings suggest that while both paradigms hold potential for combinatorial optimization, further advances in hardware capabilities and parameter calibration will be necessary to achieve reliable performance on larger instances.
Simone Faro, G. Messina, Damiano Muzzicato et al.· IEEE International Symposium...· 0 citations