  Simulating quantum many-body dynamics on classical computers is a challenging
problem due to the exponential growth of the Hilbert space. Artificial neural
networks have recently been introduced as a new tool to approximate
quantum-many body states. We benchmark the variational power of the restricted
Boltzmann machine quantum states and different shallow and deep neural
autoregressive quantum states to simulate global quench dynamics of a
non-integrable quantum Ising chain. We find that the number of parameters
required to represent the quantum state at a given accuracy increases
exponentially in time. The growth rate is only slightly affected by the network
architecture over a wide range of different design choices: shallow and deep
networks, small and large filter sizes, dilated and normal convolutions, with
and without shortcut connections.
