  We calculate the topological boundary modes found for quantum wire for a
quantum ring. For the symmetric ring we find analytical solutions for two
quasi-particles identifiable as the Majorana states and for asymmetric ring, we
have also find approximate solution. By turning on a small field at time zero,
we find a field induced oscillation of the Majorana states that was initially
localized. The range of validity of our solution, the relation between the
period of oscillation and the coin parameter and field strength, and the
encoding of a message of the on/off of the field using the Majorana states are
discussed. Our results suggest ways to reduce decoherence for small systems,
thereby providing a good candidate for quantum memory and computing as the
Majorana qubit is topologically protected.
