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

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 ABS is present at zero energy with a tiny energy fluctuation, the non-Abelian braiding property can be sustained for a larger 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 nearly zero energy ABSs with a tiny energy fluctuation might also be suitable for quantum computation.