Time-Dependent Neural Quantum States for Quantum Dynamics

Abstract

Neural Quantum States have emerged as powerful variational ansätze for modeling complex quantum systems, although their extension to real-time dynamics remains challenging. In this work, the wavefunctions of the threedimensional Quantum Harmonic Oscillator and the deuteron are parametrized through two real-valued feed-forward neural networks, representing separately the amplitude and the phase. Expectation values are estimated using Markov chain Monte Carlo sampling, ground states are optimized through Stochastic Reconfiguration, and real-time evolution is performed using the McLachlan time-dependent variational principle. After accurately reproducing the ground states of the considered systems, the optimized Neural Quantum States are used as initial conditions for time evolution. Successful dynamics are obtained for the Quantum Harmonic Oscillator, a mass-rescaled deuteron and the physical deuteron in a periodic box, with fidelities against independent benchmarks remaining above 0.9986 in all cases considered. Ultimately, these results show that Neural Quantum States provide flexible variational ansätze capable of describing accurate real-time dynamics