Scaling of Neural-Network Quantum States for Time Evolution

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. The variational power of the restricted Boltzmann machine quantum states and different shallow and deep neural autoregressive quantum states to simulate the global quench dynamics of a non-integrable quantum Ising chain is benchmarked. It is found 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, and with and without shortcut connections.