Quantum-Classical Hybrid Methods for Optimization: Lessons from Classical Decomposition

David E. Bernal Neira · 2026 · arXiv

DOI: 10.48550/arXiv.2610.27362 · open-access PDF

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

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