Coulomb-assisted braiding of Majorana fermions in a Josephson junction array

TL;DR

This paper proposes a method to braid Majorana fermions in superconducting nanowire networks by controlling Coulomb interactions through flux, enabling topological qubit operations without gate voltage control.

Contribution

It introduces a Coulomb interaction-based approach for Majorana braiding in Josephson junction arrays, bypassing the need for tunneling control via gate electrodes.

Findings

Demonstrates Coulomb interaction control via flux in Josephson junctions.

Shows non-Abelian braiding can be achieved without tunneling manipulation.

Provides a solution for topological qubit operations in superconducting systems.

Abstract

We show how to exchange (braid) Majorana fermions in a network of superconducting nanowires by control over Coulomb interactions rather than tunneling. Even though Majorana fermions are charge-neutral quasiparticles (equal to their own antiparticle), they have an effective long-range interaction through the even-odd electron number dependence of the superconducting ground state. The flux through a split Josephson junction controls this interaction via the ratio of Josephson and charging energies, with exponential sensitivity. By switching the interaction on and off in neighboring segments of a Josephson junction array, the non-Abelian braiding statistics can be realized without the need to control tunnel couplings by gate electrodes. This is a solution to the problem how to operate on topological qubits when gate voltages are screened by the superconductor.