  A general time-dependent quantum system can be driven fast from its initial
ground state to its final ground state without generating transitions by adding
a steering term to the Hamiltonian. We show how this technique can be modified
to improve on the standard quantum adiabatic algorithm by making a
single-particle and cluster approximation to the steering term. The method is
applied to a one-dimensional Ising model in a random field. For the limit of
strong disorder, the correction terms significantly enhance the probability for
the whole system to remain in the ground state for the proposed non-stoquastic
annealing protocol. We demonstrate that even when transitions occur for
stronger interaction between qubits, the most probable quantum state is one of
the lower energy states of the final Hamiltonian. Since the method can be
applied to any model, and more sophisticated approximations to the steering
term are possible, the new technique opens up an avenue for the improvement of
the quantum adiabatic algorithm.

Quantum Physics;Disordered Systems and Neural Networks