Abstract
Demonstration of Majorana non-Abelian properties is a major challenge in the field of topological superconductivity. In this work, we propose a minimal device and protocol for testing non-Abelian properties using charge-transfer operations between a quantum dot and two Majorana bound states combined with reading the parity state using a second dot. We use an adiabatic perturbation theory to find fast adiabatic paths to perform operations and to account for nonadiabatic errors. We find the ideal parameter sweep and a region in parameter space that reduces the charge-transfer operation time 1--2 orders of magnitude with respect to constant velocity driving. Using realistic parameters, we estimate that the lower bound for the timescale can be reduced to $\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$. Deviations from the ideal parameters lead to the accumulation of an undesired dynamical phase, affecting the outcome of the proposed protocol. We furthermore suggest to reduce the influence from the dynamical phase using a flux echo. The echo protocol is based on the $4\ensuremath{\pi}$ periodicity of the topological state, absent for trivial bound states.
Highlights
The realization and verification of Majorana bound states (MBSs) have received a substantial amount of attention in the past decade [1–7]
We propose a minimal device and protocol for testing non-Abelian properties using charge-transfer operations between a quantum dot and two Majorana bound states combined with reading the parity state using a second dot
We continue our study by applying adiabatic perturbation theory (APT) to the two-level system given in Eq (2), which describes two MBSs coupled to a quantum dot
Summary
The realization and verification of Majorana bound states (MBSs) have received a substantial amount of attention in the past decade [1–7]. Despite the mounting signatures consistent with MBSs, direct observation of their non-Abelian exchange properties remains a challenge in the field Such demonstration could provide smoking-gun evidence for the topological origin of MBSs, while having the outlook of being a first step in implementing protected gates in Majorana qubit devices. The principal source of error is due to splitting of the ground state degeneracy with imperfect tuning of the parameters This leads to a relative dynamical phase between the split states, reducing the visibility of the geometric phase originated from non-Abelian charge-transfer operations. As the charge-transfer process is meant to operate on long, adiabatic timescales, even a small energy splitting can lead to a substantial relative phase error, overwhelming the non-Abelian signal This presents a trade-off between driving the system slowly enough to remain in the ground state and fast enough to avoid the effects of the splitting. We instead consider the nonadiabatic effects that occur when MBSs are coupled to a driven quantum dot
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