Fusion protocol for Majorana modes in coupled quantum dots

Kavli Affiliate: Michael Wimmer

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| Summary:

In a recent breakthrough experiment (arXiv:2206.08045), Majorana zero modes
have been observed in tunnel spectroscopy for a minimal Kitaev chain
constructed from coupled quantum dots. However, as Ising anyons, Majoranas’
most fundamental property of non-Abelian statistics is yet to be detected.
Moreover, the minimal Kitaev chain is qualitatively different from topological
superconductors in that it supports Majoranas only at a sweet spot. Therefore
it is not obvious whether non-Abelian characteristics such as braiding and
fusion can be demonstrated in this platform with a reasonable level of
robustness. In this work, we theoretically propose a protocol for detecting the
Majorana fusion rules in an artificial Kitaev chain consisting of four quantum
dots. In contrast with the previous proposals for semiconductor-superconductor
hybrid nanowire platforms, here we do not rely on mesoscopic superconducting
islands, which are difficult to implement in quantum dot chains. To show the
robustness of the fusion protocol, we discuss the effects of three types of
realistic imperfections on the fusion outcomes, e.g. diabatic errors, dephasing
errors, and calibration errors. We also propose a Fermion parity readout scheme
using quantum capacitance. Our work will shed light on future experiments on
detecting the non-Abelian properties of Majorana modes in a quantum dot chain.

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