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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

Chinese

量子和物理激励的解析器为ISING和平方无限制的二进制优化模型提供专门的样本接口,但限制的优化需要更广泛的协调和认证。本调查使用经典分解来分析如何将这些解析器集成到混合量子经典算法中。我们区分正式分解、改造和减少,以及计算性管制。对于每个接口,我们询问转换保存了什么,哪些假设使外部方法融合,以及哪些认证了实施的内部常规供应。核心问题是,这些信息是否符合经典的操作算法的要求,以及混合化是否提高了解决方案的质量或总成本,足以证明其协调。Bender的混合化,列生成,缩减图表,和比较互动性方法通过将 heuristic分离

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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