  We present a local optimal control strategy to produce desired unitary
transformations. Unitary transformations are central to all quantum
computational algorithms. Many realizations of quantum computation use a
submanifold of states, comprising the quantum register, coupled by an external
driving field to a collection of additional mediating excited states. Previous
attempts to apply control theory to induce unitary transformations on the
quantum register, while successful, produced pulses that drive the population
out of the computational register at intermediate times. Leakage of population
from the register is undesirable since often the states outside the register
are prone to decay and decoherence, and populating them causes a decrease in
the final fidelity. In this work we devise a local optimal control method for
achieving target unitary transformations on a quantum register, while avoiding
intermediate leakage out of the computational submanifold. The technique
exploits a phase locking of the field to the system such as to eliminate the
undesirable excitation. This method is then applied to produce an SU(6) Fourier
transform on the vibrational levels of the ground electronic state of the
Na$_2$ molecule. The emerging mechanism uses two photon resonances to create a
transformation on the quantum register while blocking one photon resonances to
excited states.
