Analytical nonadiabatic couplings and gradients within the state-averaged orbital-optimized variational quantum eigensolver

TL;DR

This paper extends the SA-OO-VQE quantum algorithm to include efficient state-resolution and analytical gradient estimation, enabling accurate nonadiabatic coupling calculations and geometry optimizations for molecules like formaldimine.

Contribution

It introduces new methods for state-resolution and analytical gradient estimation within the SA-OO-VQE framework, enhancing its applicability to nonadiabatic processes.

Findings

Successful implementation on formaldimine molecule

Accurate location of conical intersection

Demonstrated potential for quantum chemical simulations

Abstract

In this work, we introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Ref. [S. Yalouz et al. ,Quantum Sci. Technol. 6, 024004 (2021).]). Motivated by the limitations of current quantum computers, the first extension consists in an efficient state-resolution procedure to find the SA-OO-VQE eigenstates, and not just the subspace spanned by them, while remaining in the equi-ensemble framework. This approach avoids expensive intermediate resolutions of the eigenstates by postponing this problem to the very end of the full algorithm. The second extension allows for the estimation of analytical gradients and non-adiabatic couplings, which are crucial in many practical situations ranging from the search of conical intersections to the simulation of quantum dynamics, in, for example, photoisomerization reactions. The accuracy of our new implementations is demonstrated on the formaldimine molecule CH$_2$NH (a minimal Schiff base model relevant for the study of photoisomerization in larger bio-molecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.