This study effectively presents a comprehensive analysis on the fully self-consistent GW method, highlighting its advantages in accurately predicting ionization potentials and photoelectron spectra for heavy element-containing molecules, while also addressing its computational efficiency and reliability through extensive benchmarking.

This work introduces the equation-of-motion-based method (q-sc-EOM) for calculating excitation energies on near-term quantum computers, addressing the need for reliable excited-state simulations. The method leverages self-consistent operators to ensure accuracy while satisfying the vacuum annihilation condition. Numerical simulations on small molecules demonstrate that q-sc-EOM provides precise energy differences for vertical excitations, ionization potentials, and electron affinities. Additionally, its design enhances resilience to noise, making it well-suited for implementation on Noisy Intermediate-Scale Quantum (NISQ) devices, thereby facilitating routine excited-state calculations essential for chemical and material research.

The paper presents tensor product selected configuration interaction (TPSCI), a novel method that enhances selected configuration interaction (SCI) by utilizing local molecular structures to reduce the number of SCI variables. By grouping orbitals into clusters and employing many-particle cluster states instead of Slater determinants, TPSCI achieves significant computational efficiency and accuracy. The method is particularly effective when cluster states are defined using Tucker decomposition of the SCI vector.