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  • Open Access

Gaussian process model kernels for noisy optimization in variational quantum algorithms

L. Arceci1,2,*, V. Kuzmin1, and R. van Bijnen1,2,3

  • *Contact author: luca.arceci@hotmail.com
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Phys. Rev. Research 8, 033203 – Published 18 August, 2026

DOI: https://doi.org/10.1103/p947-r9l1

Abstract

Variational quantum algorithms (VQAs) aim at solving classical or quantum optimization problems by optimizing parametrized trial states on a quantum device, based on the outcomes of noisy projective measurements. The associated optimization process benefits from an accurate modeling of the cost function landscape using Gaussian process models (GPMs), whose performance is critically affected by the choice of their kernel. Here, we introduce specialized trigonometric kernels, inspired by the observation that typical VQA cost functions display oscillatory behavior with only few frequencies. Appropriate scores to benchmark the reliability of a GPM are defined, and a systematic comparison between different kernels is carried out on prototypical problems from quantum chemistry and combinatorial optimization. We further introduce RotoGP, a sequential line-search optimizer equipped with a GPM, and test how different kernels can help mitigate noise and improve optimization convergence. Overall, we observe that the trigonometric kernels show the best performance in most of the cases under study.

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Phys. Rev. Research 8, 033203– Published 18 August, 2026
  • Received 11 October 2025
  • Accepted 16 June 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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