High precision quantum simulation of ionization energies of single valence atoms

The quantum-classical hybrid variational quantum eigensolver (VQE) algorithm is the most widely used approach in the Noisy Intermediate Scale Quantum era to obtain ground state energies of quantum many-body systems. In this pilot study, motivated by the long-term goal of calculating on quantum devices atomic properties of interest in probing new physics beyond the Standard Model of elementary particles, we extend the scope of properties that can be calculated using the VQE algorithm. In particular, we carry out a quantum simulation of the first ionization energies of light single valence atomic systems (Li, B, Be^+ , C^+ , Na, and Al), as the property occurs in the computation of several atomic properties of interest to fundamental physics via excitation energies. Electron correlation effects, which contain the relevant quantum many-body physics that we intend to capture, are weak in Li, Be^+ , and Na, whereas they are pronounced in B, C^+ , and Al. This allows us to check the versatility of the VQE algorithm in obtaining ionization energies. The theoretical and computational features that underpin the subtleties in the calculation of the ionization energies of single valence atoms have been incorporated in the present work. We benchmark our results with the full configuration interaction calculations on these systems and study their trends. Our results for Li, Be^+ , and Al (precision ∼ 1 milliHartree or less) and B, C^+ and Na ( ∼ 10s of milliHartree) demonstrate the versatility of the VQE algorithm in determining the ionization energies of single valence atoms.