Quantum Equation-of-Motion\nMethod with Single, Double,\nand Triple Excitations

The quantum equation-of-motion (qEOM) method with single\nand double\nexcitations (qEOM-SD) has been proposed to study electronically excited\nstates, but it fails to handle states dominated by double excitations.\nIn this work, we reformulate the qEOM method within the effective\nHamiltonian framework that satisfies the killer condition, and then\npresent an efficient implementation incorporating single, double,\nand triple excitations. To reduce computational complexity, we employ\npoint-group symmetry and perturbation theory to screen triple excitations,\neffectively reducing the scaling from <i>N</i><sub>o</sub><sup>6</sup><i>N</i><sub>v</sub><sup>6</sup> to <i>N</i><sub>o</sub><sup>5</sup><i>N</i><sub>v</sub><sup>5</sup>, where <i>N</i><sub>o</sub> and <i>N</i><sub>v</sub> are the numbers of occupied and virtual spin orbitals,\nrespectively. Furthermore, we account for the effect of neglected\ntriple excitations by introducing a perturbative correction to the\nexcitation energy. We apply this method to challenging cases where\nthe qEOM-SD method exhibits significant errors, such as the 2 <sup>1</sup>Δ state of CH<sup>+</sup> and the 2 <sup>1</sup>Σ\nstate of HF. Our new method achieves energy errors below 0.18 eV while\nincorporating less than 8.2% of triple excitations. Additionally,\nwe extend the operator screening technique to the quantum subspace\nexpansion method for the efficient inclusion of selected triple excitations.