Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm
<|reference_start|>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. Our open-source code is available at https://github.com/borbysh/Momentum-QNG<|reference_end|>
@article{borysenko2024application,
    title={Application of Langevin Dynamics to Advance the Quantum Natural Gradient
  Optimization Algorithm},
    author={Oleksandr Borysenko, Mykhailo Bratchenko, Ilya Lukin, Mykola Luhanko,
  Ihor Omelchenko, Andrii Sotnikov and Alessandro Lomi},
    journal={arXiv preprint arXiv:2409.01978},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.01978},
    primaryClass={quant-ph cs.LG stat.ML}
}