Quantum Algorithm Accelerates Global Optimisation of Complex Functions.

Adaptive Search, a hybrid classical algorithm, optimises multivariate functions by dynamically reducing the search space using a probability distribution and complex amplitude mapping. Analysis confirms contraction towards global optima with managed complexity, and numerical results demonstrate improved accuracy and efficiency compared to classical optimisation methods.

The efficient determination of optimal solutions to complex problems remains a significant challenge across numerous disciplines, from financial modelling to materials science. Researchers are increasingly exploring the potential of quantum computation to accelerate these processes, particularly in scenarios where classical algorithms struggle with high-dimensional problems or complex landscapes. A team led by G. Intoccia, U. Chirico, V. Schiano Di Cola, G. Pepe, and S. Cuomo, affiliated with the University of Naples Federico II and Quantum2pi S.r.l., present a novel approach in their article, “Quantum Adaptive Search: A Hybrid Quantum-Classical Algorithm for Global Optimisation of Multivariate Functions”. Their work details a hybrid algorithm that leverages quantum mechanics to intelligently refine the search area for the best solution to complex mathematical functions, subsequently employing classical optimisation techniques to achieve precise results. The algorithm, termed Quantum Adaptive Search (QAGS), utilises a complex amplitude mapping to encode solution quality, effectively focusing computational resources on the most promising regions of the solution space and demonstrating improved performance compared to purely classical methods.

Quantum-assisted optimisation represents a significant area of research, and a newly developed hybrid algorithm, termed Adaptive Search (QAGS), demonstrates potential for solving complex global optimisation problems more efficiently than classical methods. QAGS integrates the principles of quantum computation with established classical optimisation techniques, creating a synergistic approach to identifying optimal solutions within vast and intricate search spaces.

The core innovation of QAGS lies in its adaptive reduction of the search space. The algorithm estimates the probability distribution of the objective function, effectively focusing computational resources on regions most likely to contain optimal solutions. This contrasts with traditional methods which often employ a more exhaustive, and therefore less efficient, search. A quantum state encodes information regarding solution quality through complex amplitude mapping, allowing the algorithm to prioritise areas with higher potential. This quantum component facilitates exploration of the search space, while a subsequent classical optimisation process refines the solutions within the narrowed parameters.

Crucially, QAGS is designed to guarantee a contraction of the search space towards the global optimum. This is achieved through iterative refinement, where the algorithm systematically eliminates less promising regions, converging on the most viable solutions. Maintaining controlled computational complexity is also a key feature, addressing a common limitation of many quantum algorithms which can become computationally expensive as problem size increases. This controlled complexity suggests potential scalability to larger, more complex problems.

Numerical results, obtained using established benchmark functions, indicate that QAGS consistently outperforms traditional classical optimisation methods in terms of both accuracy and efficiency. The algorithm exhibits advantages in both time and space complexity, meaning it requires fewer computational resources and less time to achieve optimal solutions. This performance suggests applicability across a range of disciplines, including machine learning, where efficient optimisation is critical for training complex models. Engineering design, financial modelling, and any field requiring efficient global optimisation could also benefit from the implementation of QAGS. The algorithm’s ability to address problems intractable for conventional approaches positions it as a promising tool for tackling increasingly complex optimisation challenges.