Discrete real-time learning of quantum state subspace evolution of many-body systems in the presence of time-dependent control fields

The recent introduction of Artificial Neural Networks (ANNs) has greatly facilitated the time-dependent Variational Monte Carlo (t-VMC) method in treating many-body dynamics for both closed and open quantum systems. However, a direct implementation of the t-VMC method is prone to numerical instability in learning the time-dependent ANN quantum states. In this presentation, we will introduce the ANN-based discrete real-time learning (DRTL) method for training the many-body quantum state in the presence of time-dependent control fields. The method leverages accurate short-time quantum state propagation with the Schrödinger equation and the efficient stochastic quantum natural gradient descent algorithm in machine learning. We demonstrate the high accuracy and stability of the DRTL method for the spin excitation dynamics of L×L (L=4,6,8,10) 2D Heisenberg spin-1/2 lattices, starting with all spins in the spin-down state and driven by time-dependent control fields applied to a corner spin along with strong exchange coupling between the nearest-neighbored spins. It is found that the number of ANN parameters approximately increases quadratically with the number of spins in the system for properly following the dynamics.