Decoherence dynamics of Majorana qubits under braiding operations

TL;DR

This paper investigates how Majorana qubits lose coherence during braiding in topological superconductors, revealing the roles of bogoliubon correlations and charge fluctuations in decoherence at various temperatures.

Contribution

It provides a rigorous analysis of Majorana qubit decoherence mechanisms during braiding, highlighting the impact of local perturbations and charge fluctuations.

Findings

Majorana qubit coherence is generated through bogoliubon correlations.

Charge fluctuations cause dissipation of MZMs and correlations.

Decoherence occurs at both zero and finite temperatures.

Abstract

We study the decoherence dynamics of Majorana qubit braiding operations in a topological superconducting chain (TSC) system, in which the braiding is performed by controlling the electron-chemical potentials of the TSCs and the couplings between them. By solving rigorously the Majorana qubit dynamics, we show how the Majorana qubit coherence is generated through bogoliubon correlations formed by exchanging Majorana zero modes (MZMs) between two TSCs in braiding operations. Using the exact master equation, we demonstrate how MZMs and also the bogoliubon correlations dissipate due to charge fluctuations of the controlling gates at both the zero and finite temperatures. As a result, Majorana qubit coherence and the fermion parity conservation cannot be immune from local perturbations during braiding operations.