Excited state calculations using variational quantum eigensolver with spin-restricted ansätze and automatically-adjusted constraints

• Published in: npj computational materials 2023-01, Vol.9 (1), p.13-9, Article 13
• Main Authors: Gocho, Shigeki, Nakamura, Hajime, Kanno, Shu, Gao, Qi, Kobayashi, Takao, Inagaki, Taichi, Hatanaka, Miho
• Format: Article
• Language: English
• Subjects: 639/638/439/945; 639/638/563; Accuracy; Characterization and Evaluation of Materials; Chemistry and Materials Science; Computational chemistry; Computational Intelligence; Energy; Excitation; Materials Science; Mathematical analysis; Mathematical and Computational Engineering; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Methods; Phenols; Potential energy; Self consistent fields; Theoretical
• ISSN: 2057-3960; 2057-3960
• DOI: 10.1038/s41524-023-00965-1

The ground and excited state calculations at key geometries, such as the Frank–Condon (FC) and the conical intersection (CI) geometries, are essential for understanding photophysical properties. To compute these geometries on noisy intermediate-scale quantum devices, we proposed a strategy that combined a chemistry-inspired spin-restricted ansatz and a new excited state calculation method called the variational quantum eigensolver under automatically-adjusted constraints (VQE/AC). Unlike the conventional excited state calculation method, called the variational quantum deflation, the VQE/AC does not require the pre-determination of constraint weights and has the potential to describe smooth potential energy surfaces. To validate this strategy, we performed the excited state calculations at the FC and CI geometries of ethylene and phenol blue at the complete active space self-consistent field (CASSCF) level of theory, and found that the energy errors were at most 2 kcal mol −1 even on the ibm_kawasaki device.