Paths towards time evolution with larger neural-network quantum states

TL;DR

This paper explores the use of neural-network quantum states to simulate time evolution in many-body quantum systems, demonstrating improved methods for computational efficiency and accuracy in quantum quenches.

Contribution

It introduces the application of projected time-dependent variational Monte Carlo with neural networks, and combines it with K-FAC and minSR to enhance scalability.

Findings

p-tVMC outperforms non-projected methods

K-FAC and minSR reduce computational complexity

Applicable to neural networks with more parameters

Abstract

In recent years, the neural-network quantum states method has been investigated to study the ground state and the time evolution of many-body quantum systems. Here we expand on the investigation and consider a quantum quench from the paramagnetic to the anti-ferromagnetic phase in the tilted Ising model. We use two types of neural networks, a restricted Boltzmann machine and a feed-forward neural network. We show that for both types of networks, the projected time-dependent variational Monte Carlo (p-tVMC) method performs better than the non-projected approach. We further demonstrate that one can use K-FAC or minSR in conjunction with p-tVMC to reduce the computational complexity of the stochastic reconfiguration approach, thus allowing the use of these techniques for neural networks with more parameters.