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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

Indonesian

Penyelesai kuantum dan fisika terinspirasi menyediakan antarmuka sampling khusus untuk model optimasi biner Ising dan kuadrat yang tidak terbatas, tetapi optimasi terbatas memerlukan koordinasi dan sertifikasi yang lebih luas. Survei ini menggunakan dekomposisi klasik untuk menganalisis bagaimana penyelesai tersebut dapat diintegrasikan ke dalam algoritma kuantum-klasik hibrida. Kami membedakan dekomposisi formal, reformulasi dan reduksi, dan orchestrasi komputasi. Untuk setiap antarmuka, kami bertanya apa yang disimpan transformasi, asumsi apa yang membuat metode eksternal converge, dan mana yang mengesahkan pasokan rutin internal yang diterapkan. Pertanyaan sentral adalah apakah informasi itu memenuhi persyaratan algoritma operasi klasik dan apakah hibridisasi meningkatkan kualitas atau biaya total yang cukup untuk membenarkan koordinasi atasnya. Dekomposisi Benders, produksi

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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