  We explore the effectiveness of variational quantum circuits in simulating
the ground states of quantum many-body Hamiltonians. We show that generic
high-depth circuits, performing a sequence of layer unitaries of the same form,
can accurately approximate the desired states. We demonstrate their universal
success by using two Hamiltonian systems with very different properties: the
transverse field Ising model and the Sachdev-Ye-Kitaev model. The energy
landscape of the high-depth circuits has a proper structure for the
gradient-based optimization, i.e. the presence of local extrema -- near any
random initial points -- reaching the ground level energy. We further test the
circuit's capability of replicating random quantum states by minimizing the
Euclidean distance.
