We conduct experimental simulations of many-body quantum systems using a hybrid classical-quantum algorithm. In our setup, the wave function of the transverse field quantum Ising model is represented by a restricted Boltzmann machine. This neural network is then trained using variational Monte Carlo assisted by a D-wave quantum sampler to find the ground-state energy. Our results clearly demonstrate that already the first generation of quantum computers can be harnessed to tackle nontrivial problems concerning physics of many-body quantum systems.