Analytical Ground- and Excited-State Gradients for Molecular Electronic Structure Theory from Hybrid Quantum/Classical Methods

TL;DR

This paper introduces a method for calculating analytical ground- and excited-state energy gradients in molecular systems using hybrid quantum/classical algorithms, enabling efficient property computations for large molecules.

Contribution

It develops a Lagrangian-based approach for analytical gradients in hybrid quantum/classical methods, reducing quantum effort and enabling large-scale molecular gradient calculations.

Findings

Gradients can be computed with quantum effort similar to energy evaluation.

The method is scalable to systems with hundreds of atoms.

Quantum response contributions are significant but manageable.

Abstract

We develop analytical gradients of ground- and excited-state energies with respect to system parameters including the nuclear coordinates for the hybrid quantum/classical multistate contracted variational quantum eigensolver (MC-VQE) applied to fermionic systems. We show how the resulting response contributions to the gradient can be evaluated with a quantum effort similar to that of obtaining the VQE energy and independent of the total number of derivative parameters (e.g. number of nuclear coordinates) by adopting a Lagrangian formalism for the evaluation of the total derivative. We also demonstrate that large-step-size finite-difference treatment of directional derivatives in concert with the parameter shift rule can significantly mitigate the complexity of dealing with the quantum parameter Hessian when solving the quantum response equations. This enables the computation of analytical derivative properties of systems with hundreds of atoms, while solving an active space of their most strongly correlated orbitals on a quantum computer. We numerically demonstrate the exactness the analytical gradients and discuss the magnitude of the quantum response contributions.