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

IntroductionWe 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 fun...

Full description

Saved in:
Bibliographic Details
Published in:Frontiers in applied mathematics and statistics Vol. 11
Main Authors: Intoccia, Gabriele, Chirico, Ugo, Schiano Di Cola, Vincenzo, Pepe, Giovanni Piero, Cuomo, Salvatore
Format: Journal Article
Language:English
Published: Frontiers Media S.A 03.09.2025
Subjects:
amplitude encoding
global optimization
hybrid quantum-classical optimization
numerical analysis
quantum computing
quantum optimization algorithm
ISSN:2297-4687, 2297-4687
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:IntroductionWe 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.MethodsA 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.ResultsIn 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.DiscussionThese 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.
ISSN:2297-4687
2297-4687
DOI:10.3389/fams.2025.1662682