  Rapid preparation, manipulation, and correction of spin states with high
fidelity are requisite for quantum information processing and quantum
computing. In this paper, we propose a fast and robust approach for controlling
two spins with Heisenberg and Ising interactions. By using the concept of
shortcuts to adiabaticity, we first inverse design the driving magnetic fields
for achieving fast spin flip or generating the entangled Bell state, and
further optimize them with respect to the error and fluctuation. In particular,
the designed shortcut protocols can efficiently suppress the unwanted
transition or control error induced by anisotropic antisymmetric
Dzyaloshinskii-Moriya exchange. Several examples and comparisons are
illustrated, showing the advantages of our methods. Finally, we emphasize that
the results can be naturally extended to multiple interacting spins and other
quantum systems in an analogous fashion.
