  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 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.
