  We present a variational quantum adiabatic theorem, which states that, under
certain assumptions, the adiabatic dynamics projected onto a variational
manifold follow the instantaneous variational ground state. We focus on
low-entanglement variational manifolds and target Hamiltonians with classical
ground states. Despite the presence of highly entangled intermediate states
along the exact quantum annealing path, the variational evolution converges to
the target ground state. We demonstrate this approach with several examples
that align with our theoretical analysis.
