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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

Hindi

क्वांटम और भौतिकी-प्रोत्साहित सॉफ्टवेयर Ising और वर्ग असीमित बाइनरी अनुकूलन मॉडल के लिए विशेष नमूने इंटरफ़ेस प्रदान करते हैं, लेकिन सीमित अनुकूलन को व्यापक समन्वय और प्रमाणन की आवश्यकता होती है। यह सर्वेक्षण क्वांटम और भौतिकी-प्रोत्साहित सॉफ्टवेयर को विश्लेषण करने के लिए क्लासिक विघटन का उपयोग करता है कि ऐसे सॉफ्टवेयर हाइब्रिड क्वांटम-क्लासिक एल्गोरिथ्म में कैसे एकीकृत किए जा सकते हैं। हम औपचारिक विघटन, reformulation और reduction को अलग करते हैं, और कंप्यूटर ऑर्केस्टेशन को अलग करते हैं। प्रत्येक इंटरफ़ेस के लिए, हम पूछते हैं कि परिवर्तन क्या बना

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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