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Application of Langevin dynamics to advance the Quantum Natural Gradient optimization algorithm

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  • Borysenko, Oleksandr
  • Bratchenko, Mykhailo
  • Lukin, Ilya
  • Luhanko, Mykola
  • Omelchenko, Ihor
  • Sotnikov, Andrii
  • Lomi, Alessandro

Abstract

A Quantum Natural Gradient (QNG) algorithm for optimization of variational quantum circuits has been proposed recently. In this study, we employ the Langevin equation with a QNG stochastic force to demonstrate that its discrete-time solution gives a generalized form of the above-specified algorithm, which we call Momentum-QNG. Similar to other optimization algorithms with the momentum term, such as the Stochastic Gradient Descent with momentum, RMSProp with momentum and Adam, Momentum-QNG is more effective to escape local minima and plateaus in the variational parameter space and, therefore, demonstrates an improved performance compared to the basic QNG. In this paper we benchmark Momentum-QNG together with the basic QNG, Adam and Momentum optimizers and explore its convergence behaviour. Among the benchmarking problems studied, the best result is obtained for the quantum Sherrington–Kirkpatrick model in the strong spin glass regime. Our open-source code is available at https://github.com/borbysh/Momentum-QNG

Suggested Citation

  • Borysenko, Oleksandr & Bratchenko, Mykhailo & Lukin, Ilya & Luhanko, Mykola & Omelchenko, Ihor & Sotnikov, Andrii & Lomi, Alessandro, 2026. "Application of Langevin dynamics to advance the Quantum Natural Gradient optimization algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 682(C).
    • Handle: RePEc:eee:phsmap:v:682:y:2026:i:c:s0378437125008106
    DOI: 10.1016/j.physa.2025.131158
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    References listed on IDEAS

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    1. Alberto Peruzzo & Jarrod McClean & Peter Shadbolt & Man-Hong Yung & Xiao-Qi Zhou & Peter J. Love & Alán Aspuru-Guzik & Jeremy L. O’Brien, 2014. "A variational eigenvalue solver on a photonic quantum processor," Nature Communications, Nature, vol. 5(1), pages 1-7, September.
    2. Lijun Bo & Xiang Yu, 2025. "New Models and Methods in Dynamic Portfolio Optimization," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 13522.
    3. Wang, Peiwen & Huang, Guanglin & Lu, Wanbo, 2025. "Factor-based higher-order moment portfolio optimization," Finance Research Letters, Elsevier, vol. 85(PC).
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