  The current generation of noisy intermediate scale quantum computers
introduces new opportunities to study quantum many-body systems. In this paper,
we show that quantum circuits can provide a dramatically more efficient
representation than current classical numerics of the quantum states generated
under non-equilibrium quantum dynamics. For quantum circuits, we perform both
real- and imaginary-time evolution using an optimization algorithm that is
feasible on near-term quantum computers. We benchmark the algorithms by finding
the ground state and simulating a global quench of the transverse field Ising
model with a longitudinal field on a classical computer. Furthermore, we
implement (classically optimized) gates on a quantum processing unit and
demonstrate that our algorithm effectively captures real time evolution.
