  The challenge posed by the many-body problem in quantum physics originates
from the difficulty of describing the non-trivial correlations encoded in the
exponential complexity of the many-body wave function. Here we demonstrate that
systematic machine learning of the wave function can reduce this complexity to
a tractable computational form, for some notable cases of physical interest. We
introduce a variational representation of quantum states based on artificial
neural networks with variable number of hidden neurons. A
reinforcement-learning scheme is then demonstrated, capable of either finding
the ground-state or describing the unitary time evolution of complex
interacting quantum systems. We show that this approach achieves very high
accuracy in the description of equilibrium and dynamical properties of
prototypical interacting spins models in both one and two dimensions, thus
offering a new powerful tool to solve the quantum many-body problem.
