Quantum theory sets a bound on the minimum time required to transform from an initial state to a target state. The bound is known as quantum speed limit time. Quantum speed limit time can be used to determine the rate of quantum evolution for closed and open quantum systems. In the real world, we are dealing with open quantum systems. So, the study of quantum speed limit time for open quantum systems has particular importance. In this work, we consider the topological qubit realized by two Majorana modes. We consider the case in which the topological qubit is infuenced by the fermionic and bosonic environment. Fermionic and bosonic environments are assumed to have Ohmic-like spectral density. The quantum speed limit time is investigated for the various environments with diferent Ohmic parameters. It is observed that for the superOhmic environment with increasing Ohmic parameter the quantum speed limit time gradually reaches a constant value and so the speed of evolution reaches a uniform value. It is also observed that the quantum speed limit time reaches zero value by increasing initial time parameter for small value of Ohmic parameter while it reaches constant value for larger Ohmic parameter. The efects of the external magnetic feld on the quantum speed limit time are also studied. It is observed that with increasing magnitude of the magnetic feld, the quantum speed limit time decreases.
