Diabatic error and propagation of Majorana zero modes in interacting quantum dots systems

TL;DR

This paper investigates diabatic errors in moving Majorana zero modes within interacting quantum dot systems, emphasizing optimal potential control, effects of interactions and disorder, and practical transfer times.

Contribution

It introduces a detailed analysis of diabatic errors in realistic quantum-dot models, including Coulomb interactions and disorder, and compares different gate tuning strategies for MZM movement.

Findings

Optimal potential wall height preserves MZM localization.

Diabatic errors are significantly affected by Coulomb interactions and disorder.

MZM transfer can be achieved within practical time scales.

Abstract

Motivated by recent experimental progress in realizing Majorana zero modes (MZMs) using quantum dot systems, we investigate the diabatic errors associated with the movement of those MZMs. The movement is achieved by tuning time-dependent gate potentials applied to individual quantum dots, effectively creating a moving potential wall. To probe the optimized movement of MZMs, we calculate the experimentally accessible local density-of-states and time-dependent fidelity using many-body time-dependent numerical methods. Our analysis reveals that an optimal potential wall height is crucial to preserve the well-localized nature of the MZM during its movement. Moreover, for the first time, we analyze diabatic errors in realistic quantum-dot systems, incorporating the effects of repulsive Coulomb interactions and disorder in both hopping and pairing terms. Additionally, we provide a comparative study of diabatic errors arising from the simultaneous versus sequential tuning of multiple gates during the MZMs movement. Finally, we estimate the time scale required for MZM transfer in a six-quantum-dot system, demonstrating that MZM movement is feasible and can be completed well within the qubit's operational lifetime in practical quantum-dot setups.