  This work considers the open-loop control problem of steering a two level
quantum system from an initial to a final condition. The model of this system
evolves on the state space SU(2), having two inputs that correspond to the
complex amplitude of a resonant laser field. A symmetry preserving flat output
is constructed using a fully geometric construction and quaternion
computations. Simulation results of this flatness-based open-loop control are
provided.
