Decoherence patterns of topological qubits from Majorana modes

Abstract

We investigate the decoherence patterns of topological qubits in contact with the environment using a novel way of deriving the open system dynamics, rather than using the Feynman–Vernon approach. Each topological qubit is made up of two Majorana modes of a 1D Kitaev 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 topological qubits which are weakly coupled to fermionic/bosonic Ohmic-like environments. We find atypical patterns of quantum decoherence. In contrast to the case for non-topological qubits—which always decohere completely in all Ohmic-like environments—topological qubits decohere completely in Ohmic and sub-Ohmic environments but not in super-Ohmic ones. Moreover, we find that the fermion parities of the topological qubits, though they cannot prevent the qubit states from exhibiting decoherence in sub-Ohmic environments, can prevent thermalization turning the state into a 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.