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Quantum-Classical Hybrid Methods for Optimization: Lessons from Classical Decomposition

David E. Bernal Neira · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.27362 · cited by 0 works (OpenAlex) · open-access PDF

French

Les solvants classiques utilisent la décomposition pour analyser comment ces solvants peuvent être intégrés dans des algorithmes classiques quantiques hybrides. Nous distinguons la décomposition formelle, la reformulation et la réduction et l'orchestration informatique. Pour chaque interface, nous demandons ce que la transformation conserve, quelles hypothèses font converger la méthode externe, et ce qui certifie les fournitures de routine internes mises en œuvre. Les questions centrales sont de savoir si cette information répond aux exigences de l'algorithme classique et si l'hybridation améliore la qualité ou le coût total de la solution pour justifier sa coordination. Les méthodes de décomposition hybride de Benders, de génération de colonne, de réduction de graphique et de

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Abstract

Quantum and physics-inspired solvers provide specialized sampling interfaces for Ising and quadratic unconstrained binary optimization models, but constrained optimization requires broader coordination and certification. This survey uses classical decomposition to analyze how such solvers can be integrated into hybrid quantum-classical algorithms. We distinguish formal decomposition, reformulation and reduction, and computational orchestration. For each interface, we ask what the transformation preserves, which assumptions make the outer method converge, and which certificates the implemented inner routine supplies. The central questions are whether that information meets the classical algorithm's requirements and whether hybridization improves solution quality or total cost enough to justify its coordination overhead. Benders decomposition, column generation, graph reduction, and copositive methods illustrate this distinction by separating heuristic proposals from classical certification. We also distinguish component effects within a fixed wrapper, reduction--solver interactions, and comparisons between complete quantum-enabled and classical systems. The analyzed studies provide conditional component benefits and favorable co-design evidence, but do not establish transferable end-to-end superiority over strong classical comparators. The resulting framework identifies opportunities for constraint programming and operations research in structure-preserving design, safeguarded hybrid algorithms, and controlled benchmarking.

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Topics: Mathematical optimization, Component (thermodynamics), Quadratic unconstrained binary optimization, Computer science, Binary number, Heuristic

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