Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm

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, achieves a better convergence behavior compared to the basic QNG. In this paper we benchmark Momentum-QNG together with basic QNG, Adam and Momentum optimizers and find the optimal values of its hyperparameters. Our open-source code is available atthis https URL

@article{borysenko2025_2409.01978,
  title={ Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm },
  author={ Oleksandr Borysenko and Mykhailo Bratchenko and Ilya Lukin and Mykola Luhanko and Ihor Omelchenko and Andrii Sotnikov and Alessandro Lomi },
  journal={arXiv preprint arXiv:2409.01978},
  year={ 2025 }
}