Transformation-free generation of a quasi-diabatic representation from the state-average orbital-optimized variational quantum eigensolver

TL;DR

This paper demonstrates that the state-average orbital-optimized variational quantum eigensolver (SA-OO-VQE) can naturally produce a quasi-diabatic representation in quantum chemistry, simplifying the analysis of electronic states and nonadiabatic couplings.

Contribution

It introduces a framework to assess diabaticity in SA-OO-VQE and explores how this quantum algorithm inherently yields a quasi-diabatic representation without additional transformations.

Findings

SA-OO-VQE produces a quasi-diabatic representation "for free"

Introduces descriptors to quantify diabaticity in quantum states

Numerical illustration on formaldimine with conical intersection

Abstract

In the present work, we examine how the recent quantum-computing algorithm known as the state-average orbital-optimized variational quantum eigensolver (SA-OO-VQE), viewed within the context of quantum chemistry as a type of multiconfiguration self-consistent field (MCSCF) electronic-structure approach, exhibits a propensity to produce an ab initio quasi-diabatic representation ``for free'' if considered as a least-transformed block-diagonalization procedure, as alluded to in our previous work [S. Yalouz et al., J. Chem. Theory Comput. 18 (2022) 776] and thoroughly assessed herein. To this end, we introduce intrinsic and residual descriptors of diabaticity and re-explore the definition and linear-algebra properties - as well as their consequences on the vibronic nonadiabatic couplings - of an optimal diabatic representation within this context, and how much one may deviate from it. Such considerations are illustrated numerically on the prototypical case of formaldimine, which presents a well-known conical intersection between its ground and first-excited singlet electronic states.