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

Abstract

Despite very promising results, capturing the dynamics of complex quantum systems with neural-network ansätze 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.

Final published version

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• Dynamics of disordered quantum systems with two- and three-dimensional tensor networks
• Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice
• From quantum-enhanced to quantum-inspired Monte Carlo
• Time-dependent Neural Galerkin Method for Quantum Dynamics
• Neural-network quantum state study of the long-range antiferromagnetic Ising chain
• Efficient Optimization of Variational Autoregressive Networks with Natural Gradient
• An Empirical Study of Quantum Dynamics as a Ground State Problem with Neural Quantum States
• Adaptive quantum dynamics with the time-dependent variational Monte Carlo method