Non-Abelian statistics of Majorana zero modes in the presence of an Andreev bound state

TL;DR

This paper demonstrates that Majorana zero modes can be braided in a nanowire setup even with Andreev bound states present, showing that their non-Abelian statistics can be preserved and manipulated despite hybridization effects.

Contribution

It reveals how Andreev bound states affect Majorana braiding and shows that non-Abelian statistics can be maintained and controlled in realistic nanowire systems.

Findings

ABS can be viewed as weakly coupled MZMs

Hybridization induces arbitrary qubit rotations

Non-Abelian braiding statistics are recoverable

Abstract

Braiding Majorana zero modes (MZMs) is the key procedure toward topological quantum computation. We show such braiding can be well performed in a parallel semiconductor-superconductor nanowire structure. Considering the fact that the low-energy Andreev bound states (ABSs) usually mix with the MZMs in the present set-up, we further investigate the braiding properties of MZMs when an ABS is presented. Our numerical simulation suggests that ABS can be regarded as a pair of weakly coupled MZMs. The dynamical hybridization of MZMs plus the non-Abelian braiding of MZMs would induce an arbitrary rotation on the Bloch sphere of a single qubit. Remarkably, such rotation is manipulable since the rotation parameters could be individually modulated. Thus, the dynamic evolution can be eliminated and the non-Abelian braiding statistics, independent of the braiding time, retrieves.