General formalism of Hamiltonians for realizing a prescribed evolution   of a qubit
  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. 
D. M. Tong, Jing-Ling Chen, L. C. Kwek, C. H. Lai, and C. H. Oh