  Modern deep learning has enabled unprecedented achievements in various
domains. Nonetheless, employment of machine learning for wave function
representations is focused on more traditional architectures such as restricted
Boltzmann machines (RBMs) and fully-connected neural networks. In this letter,
we establish that contemporary deep learning architectures, in the form of deep
convolutional and recurrent networks, can efficiently represent highly
entangled quantum systems. By constructing Tensor Network equivalents of these
architectures, we identify an inherent reuse of information in the network
operation as a key trait which distinguishes them from standard Tensor Network
based representations, and which enhances their entanglement capacity. Our
results show that such architectures can support volume-law entanglement
scaling, polynomially more efficiently than presently employed RBMs. Thus,
beyond a quantification of the entanglement capacity of leading deep learning
architectures, our analysis formally motivates a shift of trending
neural-network based wave function representations closer to the
state-of-the-art in machine learning.
