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

Gabriele Intoccia^1*Salvatore Cuomo^1*Ugo Chirico¹Giovanni Piero Pepe¹Vincenzo Schiano Di Cola²

• ¹Universita degli Studi di Napoli Federico II, Naples, Italy
• ²Consiglio Nazionale delle Ricerche Area della Ricerca di Bari, Bari, Italy

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 quantumestimated 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.