  An incoherent control scheme for state control of locally controllable
quantum systems is proposed. This scheme includes three steps: (1) amplitude
amplification of the initial state by a suitable unitary transformation, (2)
projective measurement on the amplified state, and (3) final optimization by a
unitary controlled transformation. The first step increases the amplitudes of
some desired eigenstates and the corresponding probability of observing these
eigenstates, the second step projects, with high probability, the amplified
state into a desired eigenstate, and the last step steers this eigenstate into
the target state. Within this scheme, two control algorithms are presented for
two classes of quantum systems. As an example, the incoherent control scheme is
applied to the control of a hydrogen atom by an external field. The results
support the suggestion that projective measurements can serve as an effective
control and local controllability information can be used to design control
laws for quantum systems. Thus, this scheme establishes a subtle connection
between control design and controllability analysis of quantum systems and
provides an effective engineering approach for controlling quantum systems with
partial controllability information.
