Neural tensor contractions and the expressive power of deep neural quantum states

We establish a direct connection between general tensor networks and deep feed-forward artificial neural networks. The core of our results is the construction neural-network layers that efficiently perform contractions use commonly adopted nonlinear activation functions. resulting feature number edges closely match contraction complexity to be approximated. In context many-body quantum states, this result establishes states have strictly same or higher expressive power than practically usable variational As an example, we show all matrix product can written as with polynomial in bond dimension depth logarithmic system size. opposite instead does not hold true, imply there exist are expressible terms projected entangled pair but network states.