Dynamical approach to improving Majorana qubits and distinguishing them from trivial bound states

TL;DR

This paper introduces dynamical protocols involving periodic driving of quantum dots coupled to nanowires to enhance Majorana qubit coherence, reduce hybridization, and distinguish Majorana zero modes from trivial bound states through Floquet theory and numerical simulations.

Contribution

The paper proposes novel high-frequency draiding protocols to improve Majorana qubit stability and provides a dynamical test to differentiate MZMs from Andreev Bound states.

Findings

Hybridization energy reduced by several orders of magnitude.

Qubit coherence improves significantly for MZMs, deteriorates for ABSs.

Zero bias peaks become more centered at zero voltage bias.

Abstract

We study a series of dynamical protocols which involve periodically driving a quantum dot coupled to a putative nanowire hosting Majorana zero modes (MZMs) to i) reduce the hybridization between MZMs, ii) improve the coherence of the Majorana qubit with respect to $1/f$ dephasing noise and quasiparticle poisoning, and iii) provide a definitive test to differentiate Andreev Bound states (ABSs) from MZMs. The protocols are based on the notion of $draiding$ - exchanging a pair of Majoranas twice, repeatedly, at high frequency [1]. In this process, the exchanged Majorana operators acquire a robust minus sign such that terms in the Hamiltonian, linear in either operator, vanish on average. The four protocols proposed implement draiding by coupling quantum dot(s) to the end(s) of the nanowire. They are treated using Floquet theory and numerical simulations. The hybridization energy and decoherence rate are shown to be reduced by several orders of magnitude, in accordance with theoretical expectations, when the protocols are implemented on nanowires described by experimentally relevant parameters. The tunneling conductance computed in this Floquet setting reveals zero bias peaks (ZBPs) that become more centered at zero voltage bias. When these protocols are implemented on nanowires supporting ABSs that mimic MZMs in ZBP measurements, the qubit coherence $deteriorates$, in stark contrast to the case where the nanowire supports MZMs and the coherence drastically improves, thus serving as a dynamical test to distinguish MZMs from trivial bound states.