On the Simulation of Conical Intersections in Water and Methanimine Molecules Via Variational Quantum Algorithms

Abstract: We investigate the electronic structure of methanimine (CH2NH) and water (H2O) molecules in an effort to locate conical intersections (CIs) using variational quantum algorithms. Our approach implements and compares a range of hybrid quantum-classical methods, including the Variational Quantum Eigensolver (VQE), Variational Quantum Deflation (VQD), VQE with Automatically-Adjusted Constraints (VQE-AC), and we explore molecular configurations of interest using a State-Average (SA) approach. Exact Diagonalization is employed as the classical benchmark to evaluate the accuracy of the quantum algorithms. We perform simulations across a range of molecular geometries, basis sets, and active spaces to compare each algorithm's performance and accuracy, and to enhance the detectability of CIs. This work confirms the quantum variational algorithms' capability of describing conical intersections in both molecules, as long as appropriate active spaces and geometries of the molecule are chosen. We also compare the accuracy and reliability of VQE-based methods for computing excited states with classical benchmark methods, and we demonstrate good agreement within desired regions.