  We solve a model that has basic features that are desired for quantum
annealing computations: entanglement in the ground state, controllable
annealing speed, ground state energy separated by a gap during the whole
evolution, and a programmable computational problem that is encoded by
parameters of the Ising part of the spin Hamiltonian. Our solution enables
exact nonperturbative characterization of final nonadiabatic excitations,
including a scaling of their number with the annealing rate and the system
size. We prove that quantum correlations can accelerate computations and, at
the end of the annealing protocol, lead to the perfect Gibbs distribution of
all microstates.
