Paths towards time evolution with larger neural-network quantum states

Abstract

In recent years, neural-network quantum states method in conjunction with the time-dependent variational Monte Carlo have been proposed to study the dynamics of many-body quantum systems. By interpreting the quantum dynamics problem as a ground state search of an effective Hamiltonian, we show that one can use stochastic reconfiguration (SR), a remarkable method that significantly boosts the efficiency and convergence of the variational training. Furthermore, since the vanilla SR method does not scale efficiently when the size of neural-network quantum states increases, we transfer to the study of time-dependent systems, or introduce altogether, three approaches that reduce the computational complexity of the SR method, and we compare their performance: Kronecker-factored approximate curvature (K-FAC), minimum-step stochastic reconfiguration (minSR), and sequential overlapping optimization (SOO). To demonstrate the generality of these approaches, we use both the restricted Boltzmann machine and the feed-forward neural network. We consider a titled Ising model and study the quantum quench from the paramagnetic to the anti-ferromagnetic phase. We show that the three approaches allow to use stochastic reconfigurations to describe the time evolution of a many-body quantum system using a neural network with more than 10000 parameters, which would be prohibitive otherwise. For systems up to 40 spins, we observe that minSR and SOO have similar performance and both provide better accuracy than K-FAC.