Quantum Chemistry Calculations using Energy Derivatives on Quantum Computers

TL;DR

This paper introduces a method for calculating energy derivatives in quantum chemistry using variational quantum eigensolver (VQE), enabling efficient prediction of molecular properties and reaction states on near-term quantum computers.

Contribution

The authors develop a low-depth quantum circuit approach for energy derivatives in VQE, applicable to ground and excited states, with demonstrated accuracy in molecular property calculations.

Findings

Accurate energy derivatives for H₂ molecule match FCI results.

Method enables minimum energy configuration search.

Effective estimation of molecular response properties.

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.