Variational quantum algorithm for molecular geometry optimization

TL;DR

This paper presents a variational quantum algorithm that optimizes molecular geometries by jointly adjusting quantum circuits and Hamiltonian parameters, demonstrating accurate results for small molecules with quantum simulations.

Contribution

It introduces a novel variational quantum approach that explicitly considers Hamiltonian dependence on nuclear coordinates for molecular geometry optimization.

Findings

Achieved accurate equilibrium geometries for small molecules.

Demonstrated the effectiveness of adaptive quantum circuit design.

Validated results against classical quantum chemistry methods.

Abstract

Classical algorithms for predicting the equilibrium geometry of strongly correlated molecules require expensive wave function methods that become impractical already for few-atom systems. In this work, we introduce a variational quantum algorithm for finding the most stable structure of a molecule by explicitly considering the parametric dependence of the electronic Hamiltonian on the nuclear coordinates. The equilibrium geometry of the molecule is obtained by minimizing a more general cost function that depends on both the quantum circuit and the Hamiltonian parameters, which are simultaneously optimized at each step. The algorithm is applied to find the equilibrium geometries of the $\mathrm{H}_2$, $\mathrm{H}_3^+$, $\mathrm{BeH}_2$ and $\mathrm{H}_2\mathrm{O}$ molecules. The quantum circuits used to prepare the electronic ground state for each molecule were designed using an adaptive algorithm where excitation gates in the form of Givens rotations are selected according to the norm of their gradient. All quantum simulations are performed using the PennyLane library for quantum differentiable programming. The optimized geometrical parameters for the simulated molecules show an excellent agreement with their counterparts computed using classical quantum chemistry methods.