Towards Efficient Function Optimisation with Quantum–Classical Hybrid Search
- 1Department of Mathematics and Computer Sciences, Physical Sciences and Earth Sciences, University of Messina, Viale Ferdinando Stagno d’Alcontres, 31, 98166 Messina, Italy
- 2Centre for Mathematical Science, City St George’s, University of London, Northampton Square, London EC1V 0HB, UK;
- 3Department of Psychology, City St George’s, University of London, Northampton Square, London EC1V 0HB, UK;
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.
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BibTeX
@article{ziiatdinov2026towards,
title = {{Towards Efficient Function Optimisation with Quantum–Classical Hybrid Search}},
author = {Mansur Ziiatdinov and Fedor Levkovich-Maslyuk and Emmanuel M. Pothos},
journal = {Entropy (Basel, Switzerland)},
year = {2026},
month = sep,
doi = {10.3390/e28101060},
url = {https://europepmc.org/article/PMC/PMC13703397},
note = {CC BY},
}
RIS
TY - JOUR
TI - Towards Efficient Function Optimisation with Quantum–Classical Hybrid Search
AU - Mansur Ziiatdinov
AU - Fedor Levkovich-Maslyuk
AU - Emmanuel M. Pothos
PY - 2026
DA - 2026/09/01
JO - Entropy (Basel, Switzerland)
DO - 10.3390/e28101060
UR - https://europepmc.org/article/PMC/PMC13703397
AB - 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.
SN - 1099-4300
ER -