For Topological Quantum Computation non abelian anyons can be made up
of unpaired Majorana fermions. We study a simple one dimensional model
XY-Ising model where unpaired Majorana modes can be created and
manipulated. Further, we showed that a Qubit made up of degenerate
unpaired Majorana modes of the model are protected from decoherence by
environmental perturbations. Physical realization of the model using
Josephson junction quantum circuit has also been achieved.
