  Recent studies reveal that a double-quantum-dot system hosting more than two
electrons may be superior in certain aspects as compared to the traditional
case in which only two electrons are confined (a singlet-triplet qubit). We
study the electron-phonon dephasing occurring in a GaAs multi-electron
double-quantum-dot system, in a biased case in which the singlet state is
hybridized, as well as in an unbiased case in which the hybridization is
absent. We have found that while the electron-phonon dephasing rate increases
with the number of electrons confined in the unbiased case, this does not hold
in the biased case. We define a merit figure as a ratio between the exchange
energy and the dephasing rate, and have shown that in experimentally relevant
range of the exchange energy, the merit figure actually increases with the
number of electrons in the biased case. Our results show that the
multi-electron quantum-dot system has another advantage in mitigating the
effect of electron-phonon dephasing, which is previously under-appreciated in
the literature.
