Bounding errors in Neural Quantum Dynamics

Integrating the Schroedinger's equation for a Many-Body Quantum System is a challenging task whose complexity grows exponentially with the number of degrees of freedom. Variational ansatzes for the Wave-Function such as Neural Quantum States (NQS) have been shown to avoid such exponential growth in the complexity by foregoing an exact description. While NQS have produced state-of-the-art results in computations involving the physical properties of the ground- and excited-states of hamiltonians, their results when integrating the variational dynamics induced by the same hamiltonians are limited. A major issue plaguing the variational dynamics is the emergence of two different, competing timescales relating to the Many-Body Hamiltonian and to the nonlinear parametrisation of the Hilbert Space. In this contribution I will show how to quantify such time-scales and use such knowledge to better solve the problem of the variational dynamics with Neural Quantum States.