  We study the decoherence of Majorana modes of a fermion chain, where the
fermions interact with their nearest neighbours. We investigate the effect of
dissipation and dephasing on the Majorana modes of a fermionic chain. The
dissipative and dephasing noises induce the non-parity- and parity-preserving
transitions between the eigenstates of the system, respectively. Therefore,
these two types of noises lead to the different decoherence mechanisms. In each
type of noise, we discuss the low- and high-frequency regimes to describe the
different environments. We numerically calculate the dissipation and dephasing
rates in the presence of long-range interactions. We find that the decoherence
rate of interacting Majorana modes is different to that of non-interacting
modes. We show the examples that the long-range interactions can reduce the
decoherence rate. It is advantageous to the potential applications of quantum
information processing.
