  We investigate the decoherence patterns of topological qubits in contact with
the environment by a novel way of deriving the open system dynamics other than
the Feynman-Vernon. Each topological qubit is made of two Majorana modes of a
1D Kitaev's chain. These two Majorana modes interact with the environment in an
incoherent way which yields peculiar decoherence patterns of the topological
qubit. More specifically, we consider the open system dynamics of the
topological qubits which are weakly coupled to the fermionic/bosonic Ohmic-like
environments. We find atypical patterns of quantum decoherence. In contrast to
the cases of non-topological qubits for which they always decohere completely
in all Ohmic-like environments, the topological qubits decohere completely in
the Ohmic and sub-Ohmic environments but not in the super-Ohmic ones. Moreover,
we find that the fermion parities of the topological qubits though cannot
prevent the qubit states from decoherence in the sub-Ohmic environments, can
prevent from thermalization turning into Gibbs state. We also study the cases
in which each Majorana mode can couple to different Ohmic-like environments and
the time dependence of concurrence for two topological qubits.
