Readout of Majorana parity states using a quantum dot

TL;DR

This paper proposes a theoretical scheme for reading out Majorana parity states using a quantum dot, demonstrating high-fidelity measurement feasibility with precise control, and exploring its implications for topological qubit robustness.

Contribution

It introduces a novel method for projectively measuring Majorana parity states via a quantum dot, including analysis of control requirements and robustness against calibration errors.

Findings

High-fidelity parity readout is achievable with nanometer-scale control.

Oscillatory MBS splitting does not hinder readout if gate control is precise.

The scheme can distinguish valid from invalid parity measurements, aiding topological qubit validation.

Abstract

We theoretically examine a scheme for projectively reading out the parity state of a pair of Majorana bound states (MBS) using a tunnel coupled quantum dot. The dot is coupled to one end of the topological wire but isolated from any reservoir, and is capacitively coupled to a charge sensor for measurement. The combined parity of the MBS-dot system is conserved and charge transfer between the MBS and dot only occurs through resonant tunnelling. Resonance is controlled by the dot potential through a local gate and by the MBS energy splitting due to the overlap of the MBS pair wavefunctions. The latter splitting can be tuned from zero (topologically protected regime) to a finite value by gate-driven shortening of the topological wire. Simulations show that the oscillatory nature of the MBS splitting is not a fundamental obstacle to readout, but requires precise gate control of the MBS spatial position and dot potential. With experimentally realistic parameters, we find that high-fidelity parity readout is achievable given nanometer-scale spatial control of the MBS, and that there is a tradeoff between required precisions of temporal and spatial control. Use of the scheme to measure the MBS splitting versus separation would present a clear signature of topological order, and could be used to test the robustness of this order to spatial motion, a key requirement in certain schemes for scalable topological qubits. We show how the scheme can be extended to distinguish valid parity measurements from invalid ones due to gate calibration errors.