Many-Body-Expansion Based on Variational Quantum Eigensolver and Deflation for Dynamical Correlation

Abstract: In this study, we utilize the many-body expansion (MBE) framework to decompose electronic structures into fragments by incrementing the virtual orbitals. Our work aims to accurately solve the ground and excited state energies of each fragment using the variational quantum eigensolver and deflation algorithms. Although our approach is primarily based on unitary coupled cluster singles and doubles (UCCSD) and a generalization thereof, we also introduce modifications and approximations to conserve quantum resources in MBE by partially generalizing the UCCSD operator and neglecting the relaxation of the reference states. As a proof of concept, we investigate the potential energy surfaces for the bond-breaking processes of the ground state of two molecules ($\rm H_2O$ and $\rm N_2$) and calculate the ground and excited state energies of three molecules (LiH, CH$^+$, and $\rm H_2O$). The results demonstrate that our approach can, in principle, provide reliable descriptions in all tests, including strongly correlated systems, when appropriate approximations are chosen. Additionally, we perform model simulations to investigate the impact of shot noise on the total MBE energy and show that precise energy estimation is crucial for lower-order MBE fragments.