Quantum adaptive search: a hybrid quantum-classical algorithm for global optimization of multivariate functions

Introduction: We present Quantum Adaptive Search (QAGS), a hybrid quantum-classical algorithm for global optimization of multivariate functions. The method employs an adaptive mechanism that dynamically narrows the search space based on a quantum-estimated probability distribution of the objective function. Methods: A quantum state encodes information about solution quality through a complex-amplitude mapping, enabling identification of promising regions and progressive tightening of the search bounds; a classical optimizer then performs local refinement. The analysis shows contraction of the search space toward global optima with controlled computational complexity. Results: In simulation on standard benchmarks (Rastrigin, Styblinski-Tang, Rosenbrock), QAGS attains solutions at or near the true minima with very small absolute errors. Against an Adaptive Grid Search on the Sphere function, QAGS achieves comparable accuracy and shows increasing efficiency with dimensionality. Discussion: These results indicate that amplitude-encoded region selection combined with classical refinement effectively contracts the search space and can reduce time and space requirements, especially at higher dimensions, while practical hardware implementations of amplitude encoding remain challenging.