  We present a novel approach for analytically reducing a family of
time-dependent multi-state quantum control problems to two-state systems. The
presented method translates between $SU(2)XSU(2)$ controlled $n^{2}$-state
systems and two-state systems, such that the former undergo complete population
transfer (CPT) if and only if the latter reach specific states. For even n, the
method translates any two-state CPT scheme to CPT schemes in $n^{2}$-state
systems. In particular, facilitating CPT in a four-state system via real
time-dependent nearest-neighbors couplings is reduced to facilitating CPT in a
two-level system. Furthermore, we show that the method can be used for operator
control, and provide conditions for producing several universal gates for
quantum computation as an example. In addition, we indicate a basis for
utilizing the method in optimal control problems.
