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

Understand

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.