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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

Japanese

量子および物理学にインスパイアされたソーラーは、ISINGおよび平方無制限バイナリ最適化モデルのための専門サンプルインタフェースを提供しますが、制限された最適化はより広範な調整と認証を必要とします。この調査では、クラシック分解を使用して、そのようなソーラーがハイブリッド量子クラシックアルゴリズムに組み込まれる方法を分析します。我々は、形式的な分解、再構成および減少、およびコンピュータオキストレーションを区別します。それぞれのインターフェイスでは、私たちは、変換が保存するもの、外部方法が合併する仮定、および実施された内部ルーティング供給を証明するものについて質問します。中央の質問は

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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