Braiding Majoranas in a linear quantum dot-superconductor array: Mitigating the errors from Coulomb repulsion and residual tunneling

TL;DR

This paper proposes a minimal linear quantum dot-superconductor array setup for braiding Majorana zero modes, addressing error mitigation from Coulomb repulsion and tunneling through optimal control, and suggests experimental detection methods.

Contribution

It introduces a novel minimal braiding scheme in quantum dot arrays and demonstrates error mitigation strategies specific to quantum dot devices.

Findings

Errors from Coulomb repulsion and tunneling can be mitigated by optimal control.

Proposes experimentally accessible methods to find optimal braiding conditions.

Predicts signatures indicating successful Majorana braiding.

Abstract

Exchanging the positions of two non-Abelian anyons transforms between many-body wavefunctions within a degenerate ground-state manifold. This behavior is fundamentally distinct from fermions, bosons and Abelian anyons. Recently, quantum dot-superconductor arrays have emerged as a promising platform for creating topological Kitaev chains that can host non-Abelian Majorana zero modes. In this work, we propose a minimal braiding setup in a linear array of quantum dots consisting of two minimal Kitaev chains coupled through an ancillary, normal quantum dot. We focus on the physical effects that are peculiar to quantum dot devices, such as interdot Coulomb repulsion and residual single electron tunneling. We find that the errors caused by either of these effects can be efficiently mitigated by optimal control of the ancillary quantum dot that mediates the exchange of the non-Abelian anyons. Moreover, we propose experimentally accessible methods to find this optimal operating regime and predict signatures of a successful Majorana braiding experiment.