Analytical energy gradient for state-averaged orbital-optimized variational quantum eigensolvers and its application to a photochemical reaction

TL;DR

This paper develops an analytical energy gradient method for state-averaged orbital-optimized variational quantum eigensolvers, enabling quantum computation of photochemical reaction pathways including conical intersections.

Contribution

It extends the theory of SA-OO-VQE to include analytical gradients, facilitating the study of photochemical reactions on near-term quantum computers.

Findings

Successfully applied to model cis-trans isomerization

Accurately captured conical intersection points

Demonstrated feasibility of quantum algorithms for photochemistry

Abstract

Elucidating photochemical reactions is vital to understand various biochemical phenomena and develop functional materials such as artificial photosynthesis and organic solar cells, albeit its notorious difficulty by both experiments and theories. The best theoretical way so far to analyze photochemical reactions at the level of ab initio electronic structure is the state-averaged multi-configurational self-consistent field (SA-MCSCF) method. However, the exponential computational cost of classical computers with the increasing number of molecular orbitals hinders applications of SA-MCSCF for large systems we are interested in. Utilizing quantum computers was recently proposed as a promising approach to overcome such computational cost, dubbed as state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE). Here we extend a theory of SA-OO-VQE so that analytical gradients of energy can be evaluated by standard techniques that are feasible with near-term quantum computers. The analytical gradients, known only for the state-specific OO-VQE in previous studies, allow us to determine various characteristics of photochemical reactions such as the conical intersection (CI) points. We perform a proof-of-principle calculation of our methods by applying it to the photochemical cis-trans isomerization of 1,3,3,3-tetrafluoropropene. Numerical simulations of quantum circuits and measurements can correctly capture the photochemical reaction pathway of this model system, including the CI points. Our results illustrate the possibility of leveraging quantum computers for studying photochemical reactions.