  The quantum equation-of-motion (qEOM) method with singles and doubles has
been suggested to study electronically excited states while it fails to predict
the excitation energies dominated by double excitations. In this work, we
present an efficient implementation of the qEOM method with single, double and
triple excitations. In order to reduce the computational complexity, we utilize
the point group symmetry and perturbation theory to screen triple excitation
operators, and the scaling is reduced from $N_o^6N_v^6$ to $N_o^5N_v^5$.
Furthermore, we introduce a perturbation correction to the excitation energy to
account for the effect of ignored triple excitation operators. We apply this
method to study challenging cases, for which the qEOM-SD method exhibits large
errors, such as the 2 $^1\Delta$ excited state of $\rm{CH}^+$ and the 2
$^1\Sigma$ state of $\rm{H}_8$ molecule. Our new method yields the energy
errors less than 0.18 eV.
