Paper ID: 2409.01978

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

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

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 this https URL

Submitted: Sep 3, 2024