  Artificial neural networks have been successfully incorporated into
variational Monte Carlo method (VMC) to study quantum many-body systems.
However, there have been few systematic studies of exploring quantum many-body
physics using deep neural networks (DNNs), despite of the tremendous success
enjoyed by DNNs in many other areas in recent years. One main challenge of
implementing DNN in VMC is the inefficiency of optimizing such networks with
large number of parameters. We introduce an importance sampling gradient
optimization (ISGO) algorithm, which significantly improves the computational
speed of training DNN in VMC. We design an efficient convolutional DNN
architecture to compute the ground state of a one-dimensional (1D) SU($N$) spin
chain. Our numerical results of the ground-state energies with up to 16 layers
of DNN show excellent agreement with the Bethe-Ansatz exact solution.
Furthermore, we also calculate the loop correlation function using the wave
function obtained. Our work demonstrates the feasibility and advantages of
applying DNNs to numerical quantum many-body calculations.
