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
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- github.com/borbysh/momentum-qngOfficialIn papernone★ 1
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, 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 at https://github.com/borbysh/Momentum-QNG