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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

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Los solventes cuánticos e inspirados en la física proporcionan interfaces de muestreo especializadas para modelos de optimización binaria no restringidos de Ising y cuadrados, pero la optimización restringida requiere una mayor coordinación y certificación. Esta encuesta utiliza la descomposición clásica para analizar cómo se pueden integrar tales solventes en algoritmos cuánticos híbridos clásicos. Distinguimos la descomposición formal, la reformulación y la reducción, y la orquestación computacional. Para cada interfaz, preguntamos qué preserva la transformación, qué suposiciones hacen converger el método externo, y qué certifica los suministros de rutina internos implementados. Las preguntas centrales son si esa información cumple con los requisitos del algoritmo clásico y si la hibridación mejora la calidad o el coste total de

Machine translation (Meta M2M100); the English original follows.

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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