  Despite the huge theoretical potential of neural quantum states, their use in
describing generic, highly-correlated quantum many-body systems still often
poses practical difficulties. Customized network architectures are under active
investigation to address these issues. For a guided search of suited network
architectures a deepened understanding of the link between neural network
properties and attributes of the physical system one is trying to describe, is
imperative. Drawing inspiration from the field of machine learning, in this
work we show how information propagation in deep neural networks impacts the
physical entanglement properties of deep neural quantum states. In fact, we
link a previously identified information propagation phase transition of a
neural network to a similar transition of entanglement in neural quantum
states. With this bridge we can identify optimal neural quantum state
hyperparameter regimes for representing area as well as volume law entangled
states. The former are easily accessed by alternative methods, such as tensor
network representations, at least in low physical dimensions, while the latter
are challenging to describe generally due to their extensive quantum
entanglement. This advance of our understanding of network configurations for
accurate quantum state representation helps to develop effective
representations to deal with volume-law quantum states, and we apply these
findings to describe the ground state (area law state) vs. the excited state
(volume law state) properties of the prototypical next-nearest neighbor
spin-1/2 Heisenberg model.
