Neural Projected Quantum Dynamics: a systematic study.

Efficient simulation of large-scale quantum dynamics is crucial for material science, quantum chemistry, and quantum information processing. While tensor network methods excel in one-dimensional systems, their extension to higher dimensions or volume-law phases remains challenging. At the cross roads between machine learning and quantum physics, Neural Quantum States (NQS) have emerged as a promising alternative, capable of simultaneously encoding arbitrary degrees of entanglement while remaining computationally tractable in higher dimensions.

Despite achieving state-of-the-art results in ground-state problems, NQS have yet to deliver significant improvements for quantum dynamics. Progress in this direction has been hindered by the intrinsic instability of the time-dependent variational Monte Carlo (t-VMC) method, the standard for variational quantum dynamics. Contributing to such instability are the stiffness of the tVMC equation and the systematic statistical bias inherent to its evaluation.

This work presents an in-depth study of projected-tVMC (p-tVMC): a novel approach overcoming the key limitations of t-VMC by decoupling the problem of discretization of the physical dynamics from the nonlinear optimization of the variational ansatz. By identifying stable stochastic estimators for infidelity minimization, introducing adaptive regularization for natural gradient descent, and developing high-order integration schemes exploiting the algebraic structure of the p-tVMC optimization problem, we achieve, for the first time, robust state-of-the-art performance with p-tVMC.

Our results establish p-tVMC as a scalable framework for large-scale quantum dynamics, offering a compelling solution to push the boundaries of quantum simulations.