🤖 AI Summary
To address the challenges of premature convergence to local minima and gradient vanishing in variational quantum circuit training, this paper introduces Langevin dynamics into the quantum natural gradient (QNG) optimization framework for the first time, proposing Momentum-QNG—a generalized QNG algorithm incorporating explicit stochastic thermal noise and momentum. Theoretically, we derive its discrete iterative update rule. Extensive experiments across diverse tasks—including variational quantum eigensolvers (VQE) and quantum machine learning (QML)—demonstrate that Momentum-QNG significantly outperforms standard QNG, Adam, and classical momentum methods in convergence speed, final accuracy, and training robustness. We open-source the implementation and conduct a comprehensive hyperparameter sensitivity analysis to identify optimal configurations. Empirical results confirm substantial improvements in generalization capability and training stability.
📝 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