Neural Projected Quantum Dynamics: a systematic study

TL;DR

This paper advances the simulation of large-scale 2D quantum dynamics by improving the projected time-dependent Variational Monte Carlo method, analyzing its convergence, variance, and error scaling, and demonstrating state-of-the-art results on Ising quench benchmarks.

Contribution

It provides a systematic analysis and significant improvements to p-tVMC, establishing it as a powerful tool for simulating complex quantum dynamics.

Findings

Achieved state-of-the-art performance on 2D Ising quench.

Provided formalization and analysis of stochastic estimators.

Demonstrated improved convergence and error scaling of p-tVMC.

Abstract

We investigate the challenge of classical simulation of unitary quantum dynamics with variational Monte Carlo approaches, addressing the instabilities and high computational demands of existing methods. By systematically analyzing the convergence of stochastic infidelity optimizations, examining the variance properties of key stochastic estimators, and evaluating the error scaling of multiple dynamical discretization schemes, we provide a thorough formalization and significant improvements to the projected time-dependent Variational Monte Carlo (p-tVMC) method. We benchmark our approach on a two-dimensional Ising quench, achieving state-of-the-art performance. This work establishes p-tVMC as a powerful framework for simulating the dynamics of large-scale two-dimensional quantum systems, surpassing alternative VMC strategies on the investigated benchmark problems.