  We explore the role of entanglement in adiabatic quantum optimization by
performing approximate simulations of the real-time evolution of a quantum
system while limiting the amount of entanglement. To classically simulate the
time evolution of the system with a limited amount of entanglement, we
represent the quantum state using matrix-product states and projected
entangled-pair states. We show that the probability of finding the ground state
of an Ising spin glass on either a planar or non-planar two-dimensional graph
increases rapidly as the amount of entanglement in the state is increased.
Furthermore, we propose evolution in complex time as a way to improve simulated
adiabatic evolution and mimic the effects of thermal cooling of the quantum
annealer.
