Non-local response in the disordered Majorana chain

TL;DR

This paper investigates how disorder affects Majorana zero-modes in nanowires, revealing non-local responses to local perturbations and proposing a time-scale window for preserving quantum information during manipulations.

Contribution

It demonstrates that disordered Majorana chains exhibit non-local responses to local perturbations and identifies an optimal time window for quantum information preservation.

Findings

Disordered Majorana chains undergo non-local responses via multi-level Landau-Zener transitions.

Quantum information disperses among zero-modes during adiabatic manipulations.

An intermediate time-scale window can approximately preserve quantum information.

Abstract

The prospects for realizing a topological quantum computer have brightened since the apparent detection of Majorana fermions at the ends of semiconducting nanowires. These Majorana zero-modes persist in the presence of the strong disorder that may be present in such systems, protected by the mobility gap of localized systems. Recent proposals to manipulate quantum information in a Majorana chain involve adiabatically adjusting gate voltages in one-dimensional nanowire networks. However, as we show, in the adiabatic limit, a disordered system with multiple zero-mode Majorana fermions will undergo a non-local response to a local perturbation via a multi-level Landau-Zener transition. This will disperse the quantum information stored in the target zero-modes amongst other zero-modes that are present in the system, complicating the realization of controlled gates. There is however a solution that may work in practice: we show that there is an optimum window of intermediate time-scales during which the quantum information is approximately preserved under manipulation.