Quantum Adaptive Search: A Hybrid Quantum-Classical Algorithm for Global Optimization of Multivariate Functions

TL;DR

Quantum Adaptive Search (QAGS) is a hybrid quantum-classical algorithm that efficiently narrows down the search space for global optimization of multivariate functions, outperforming classical methods in accuracy and resource usage.

Contribution

Introduces QAGS, a novel hybrid quantum-classical algorithm that adaptively refines the search space using quantum probability distributions for global optimization.

Findings

QAGS achieves higher accuracy than classical methods.

QAGS reduces time and space complexity.

QAGS guarantees contraction of the search space toward global optima.

Abstract

This work presents Quantum Adaptive Search (QAGS), a hybrid quantum-classical algorithm for the 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. A quantum state encodes information about solution quality through an appropriate complex amplitude mapping, enabling the identification of the most promising regions, and thus progressively tightening the search bounds; then a classical optimizer performs local refinement of the solution. The analysis demonstrates that QAGS ensures a contraction of the search space toward global optima, with controlled computational complexity. The numerical results on the benchmark functions show that, compared to the classical methods, QAGS achieves higher accuracy while offering advantages in both time and space complexity.