Non-Markovian decoherence dynamics of Majorana zero modes and Majorana qubits

Abstract

In this thesis We use the exact master equation approach to investigate the decoherence dynamics of Majorana zero modes in the Kitaev model a 1D p-wave spinless topological superconducting chain (TSC) that is disturbed by gate-induced charge fluctuations The exact master equation is derived by extending Feynman-Vernon influenced functional technique to fermionic open systems involving pairing excitations We obtain the exact master equation for the zero-energy Bogoliubov quasiparticle (bogoliubon) in the TSC and then transfer it into the master equation for the Majorana zero modes Within this exact master equation formalism we can describe in detail the non-Markovian decoherence dynamics of the zero-energy bogoliubon as well as Majorana zero modes under local perturbations We also study the decoherence dynamics of Majorana qubit braiding operations in a 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 between two TSCs in braiding operations We also demonstrate with the exact master equation how Majorana zero modes and also the bogoliubon correlations dissipate due to charge fluctuations of the controlling gates at both the zero and finite temperatures

Date of Award	2020
Original language	English
Supervisor	Wei-Min Zhang (Supervisor)