City Research Online

Abstract

Finding the global minimum of a function with many local extrema is well known to be a challenging computational task. We propose a hybrid quantum–classical algorithm for this optimisation problem, based on a combination of Grover quantum search and the classical Newton–Raphson method. The approach is tailored to situations with a large number of false minima. The main idea is to use quantum search to efficiently locate the vicinity of the true optimum, after which a classical algorithm can solve the problem in only a few iterations. We specifically address the nontrivial question of choosing the discretisation of the function domain, which is critical for quantum approaches to optimisation of continuous functions. While we do not expect that this method will always be superior, we identify a paradigmatic case of a function for which we demonstrate that, remarkably, our hybrid method quadratically outperforms a purely classical approach (measuring performance by the number of function/oracle calls). We evaluate key performance metrics of the algorithm in numerical experiments. We furthermore discuss its possible extensions as well as the potential relevance of hybrid approaches in the context of quantum cognition.

Publication Type:	Article
Additional Information:	© 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
Publisher Keywords:	quantum computing; continuous function optimisation; Grover’s algorithm; Newton–Raphson’s method
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Departments:	School of Science & Technology School of Science & Technology > Department of Mathematics School of Health & Medical Sciences > Department of Psychology & Neuroscience
SWORD Depositor:	Symplectic Administrator

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