  We examine the usefulness of applying neural networks as a variational state
ansatz for many-body quantum systems in the context of quantum
information-processing tasks. In the neural network state ansatz, the complex
amplitude function of a quantum state is computed by a neural network. The
resulting multipartite entanglement structure captured by this ansatz has
proven rich enough to describe the ground states and unitary dynamics of
various physical systems of interest. In the present paper, we initiate the
study of neural network states in quantum information-processing tasks. We
demonstrate that neural network states are capable of efficiently representing
quantum codes for quantum information transmission and quantum error
correction, supplying further evidence for the usefulness of neural network
states to describe multipartite entanglement. In particular, we show the
following main results: a) Neural network states yield quantum codes with a
high coherent information for two important quantum channels, the generalized
amplitude damping channel and the dephrasure channel. These codes outperform
all other known codes for these channels, and cannot be found using a direct
parametrization of the quantum state. b) For the depolarizing channel, the
neural network state ansatz reliably finds the best known codes given by
repetition codes. c) Neural network states can be used to represent absolutely
maximally entangled states, a special type of quantum error-correcting codes.
In all three cases, the neural network state ansatz provides an efficient and
versatile means as a variational parametrization of these highly entangled
states.
