  We develop a machine learning method to construct accurate ground-state wave
functions of strongly interacting and entangled quantum spin as well as
fermionic models on lattices. A restricted Boltzmann machine algorithm in the
form of an artificial neural network is combined with a conventional
variational Monte Carlo method with pair product (geminal) wave functions and
quantum number projections. The combination allows an application of the
machine learning scheme to interacting fermionic systems. The combined method
substantially improves the accuracy beyond that ever achieved by each method
separately, in the Heisenberg as well as Hubbard models on square lattices,
thus proving its power as a highly accurate quantum many-body solver.
