Quantum Chemistry Calculations using Energy Derivatives on Quantum Computers

Abstract: Quantum chemistry calculations such as the prediction of molecular properties and modeling of chemical reactions are a few of the critical areas where near-term quantum computers can showcase quantum advantage. We present a method to calculate energy derivatives for both ground state and excited state energies with respect to the parameters of a chemical system based on the framework of the variational quantum eigensolver (VQE). A low-depth implementation of quantum circuits within the hybrid variational paradigm is designed, and their computational costs are analyzed. We showcase the effectiveness of our method by incorporating it in some key quantum chemistry applications of energy derivatives, such as to perform minimum energy configuration search and estimate molecular response properties estimation of H$_2$ molecule, and also to find the transition state of H$_2$ + H $\leftrightarrow$ H + H$_2$ reaction. The obtained results are shown to be in complete agreement with their respective full configuration interaction (FCI) values.