Decoherence Patterns of Topological Qubits from Majorana Modes

TL;DR

This paper explores the unique decoherence behaviors of topological qubits made from Majorana modes, revealing environment-dependent patterns that differ from non-topological qubits, with implications for quantum information stability.

Contribution

It introduces a novel method for analyzing open system dynamics of topological qubits and uncovers environment-specific decoherence patterns and the role of fermion parity in thermalization prevention.

Findings

Topological qubits decohere completely in Ohmic and sub-Ohmic environments.

In super-Ohmic environments, topological qubits do not fully decohere.

Fermion parity can prevent thermalization but not decoherence in sub-Ohmic environments.

Abstract

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.