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

• URL: http://arxiv.org/abs/2409.01978v2
• Date: Wed, 11 Sep 2024 09:54:19 GMT
• Title: Application of Langevin Dynamics to Advance the Quantum Natural Gradient Optimization Algorithm
• Authors: Oleksandr Borysenko, Mykhailo Bratchenko, Ilya Lukin, Mykola Luhanko, Ihor Omelchenko, Andrii Sotnikov, Alessandro Lomi,
• Abstract summary: 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 force to demonstrate that its discrete-time solution gives a generalized form, which we call Momentum-QNG.
• Score: 47.47843839099175
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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. Our open-source code is available at https://github.com/borbysh/Momentum-QNG

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