  We investigate the inverse problem concerning the evolution of a qubit
system, specifically we consider how one can establish the Hamiltonians that
account for the evolution of a qubit along a prescribed path in the projected
Hilbert space. For a given path, there are infinite Hamiltonians which can
realize the same evolution. A general form of the Hamiltonians is constructed
in which one may select the desired one for implementing a prescribed
evolution. This scheme can be generalized to higher dimensional systems.
