Dynamics with autoregressive neural quantum states: application to critical quench dynamics

TL;DR

This paper introduces a stable autoregressive neural network approach for simulating long-time quantum dynamics, successfully applying it to the 2D quantum Ising model and confirming known scaling laws.

Contribution

It proposes a normalization-based autoregressive neural network scheme that improves stability in simulating quantum dynamics, addressing noise issues in previous methods.

Findings

Excellent agreement with exact dynamics for small systems

Recovered scaling laws consistent with other variational methods

Demonstrated stability for long-time quantum simulations

Abstract

Despite very promising results, capturing the dynamics of complex quantum systems with neural-network ans\"atze has been plagued by several problems, one of which being stochastic noise that makes the dynamics unstable and highly dependent on some regularization hyperparameters. We present an alternative general scheme that enables one to capture long-time dynamics of quantum systems in a stable fashion, provided the neural-network ansatz is normalized, which can be ensured by the autoregressive property of the chosen ansatz. We then apply the scheme to time-dependent quench dynamics by investigating the Kibble-Zurek mechanism in the two-dimensional quantum Ising model. We find an excellent agreement with exact dynamics for small systems and are able to recover scaling laws in agreement with other variational methods.