Effects of disorder on Coulomb-assisted braiding of Majorana zero modes

TL;DR

This paper demonstrates that Coulomb-assisted braiding of Majorana zero modes remains effective even with disorder-induced accidental modes, provided their couplings are sufficiently weak, ensuring robust quantum operations.

Contribution

It shows that braiding protocols are resilient to disorder-induced accidental Majorana modes, expanding the feasibility of topological quantum computing in realistic disordered systems.

Findings

Braiding errors are small if couplings to accidental modes are weak.

Coulomb-assisted braiding protocol remains effective despite disorder.

Accidental Majorana modes do not significantly impair braiding fidelity.

Abstract

Majorana zero modes in one-dimensional topological superconductors obey non-Abelian braiding statistics. Braiding manipulations can be realized by controlling Coulomb couplings in hybrid Majorana-transmon devices. However, strong disorder may induce accidental Majorana modes, which are expected to have detrimental effects on braiding statistics. Nevertheless, we show that the Coulomb-assisted braiding protocol is efficiently realized also in the presence of accidental modes. The errors occurring during the braiding cycle are small if the couplings of the computational Majorana modes to the accidental ones are much weaker than the maximum Coulomb coupling.