  Based on the principle of linearized stability proposed by Lyapounov, we
investigate the robustness of Majorana zero energy state (MZES), which plays an
important role in topological quantum computation. We show that the MZES is not
enough robust against the external perturbations, because mathematically it is
critical stable instead of the asymptotic stable, only the states with
asymptotic stability can be regarded as robustness, so the MZES can not be used
to carry quantum information in topological quantum computation. Our study is
different from previous works that usually make the numerical test by some
special perturbations, our analytical derivation is suitable for arbitrary
perturbations. As an example, we demonstrate it by the stability analysis of
MZES in the spin-orbit coupled semiconductor/ superconductor junction.
