  In a recent breakthrough experiment [Nature (London) 614, 445 (2023)],
signatures of 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.
