  One of the difficulties in adiabatic quantum computation is the limit on the
computation time. Here we propose two schemes to speed-up the adiabatic
evolution. To apply this controlled adiabatic evolution to adiabatic quantum
computation, we design one of the schemes without any prior knowledge of the
instantaneous eigenstates of the final Hamiltonian. Whereas in another scheme,
the control is constructed with the instantaneous eigenstate that is the target
state of the control. As an illustration, we study a two-level system driven by
a time-dependent magnetic field under the control. The physics behind the
control scheme is explained.
