Quantifying the non-Abelian property of Andreev bound states in inhomogeneous Majorana nanowires

TL;DR

This paper investigates how trivial Andreev bound states in inhomogeneous Majorana nanowires can exhibit non-Abelian braiding properties, potentially enabling topological quantum computation even without Majorana zero modes.

Contribution

It systematically analyzes the braiding properties of Andreev bound states in inhomogeneous nanowires and identifies conditions where they can mimic Majorana zero modes for quantum computing.

Findings

Trivial ABSs at zero energy can sustain non-Abelian braiding with minimal dynamic phase interference.

Under certain conditions, ABSs can outperform MZMs in braiding stability.

ABSs may be viable for topological quantum computation in realistic systems.

Abstract

Non-Abelian braiding is a key property of Majorana zero modes (MZMs) that can be utilized for topological quantum computation. However, the presence of trivial Andreev bound states (ABSs) in topological superconductors can hinder the non-Abelian braiding of MZMs. We systematically investigate the braiding properties of ABSs induced by various inhomogeneous potentials in nanowires and quantify the main obstacles to non-Abelian braiding. We find that if a trivial ABSs is present at zero energy with a tiny energy fluctuation, their non-Abelian braiding property can be sustained for a longer braiding time cost, since the undesired dynamic phase is suppressed. Under certain conditions, the non-Abelian braiding of ABSs can even surpass that of MZMs in realistic systems, suggesting that ABSs might also be suitable for topological quantum computation.