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

TL;DR

The paper addresses the challenge of nonadiabatic dynamics by seeking a robust diabatic framework without post-processing. It shows that state-average orbital-optimized VQE (SA-OO-VQE) acts as a least-transformed block-diagonalizer, producing an ab initio quasi-diabatic representation for a two-state subspace. Numerical demonstrations on formaldimine reveal that the resulting diabatic basis is nearly optimal, with descriptors $d(\mathbf{q})$ and $r(\mathbf{q})$ remaining small and nonadiabatic couplings appropriately partitioned into removable and nonremovable parts. This transformation-free diabaticity has potential to enable direct quantum-dynamics simulations (e.g., DD-vMCG, MCTDH) and can be extended to larger state spaces and NAC-aware cost functions, marking a practical advance for simulating photochemical processes.

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.

Figures (9)

• Figure 1: Schematic graphical summary of the essential quantities involved in this work and their relations. In red, the usual path to get (quasi-)diabatic states from SA-CASSCF. In blue, the path taken in this work using SA-OO-VQE. 'CI-matrix' refers to the first two CI-coefficient column-vectors, corresponding to the two states of the model/target subspaces.
• Figure 2: Schematic representation of the two angular spherical coordinates and Cartesian frame defining the geometry exploration of the formaldimine molecule in this work.
• Figure 3: Ground- and excited-state energy maps in the adiabatic (dark and light blue dotted lines) and diabatic (orange and yellow dotted lines) representations.
• Figure 4: Top panel: off-diagonal coupling element in the diabatic representation, $W(\bm{q}) = H_{\rm AB}(\bm{q}) = H_{\rm AB}(\bm{q})$. Note that $W(\bm{q})=0$ for both $\phi=0$ and $\phi=90$ degree. Bottom panel: diagonal diabatic entries, $D(\bm{q})=(H_{\rm BB}(\bm{q}) - H_{\rm AA}(\bm{q}))/2$.
• Figure 5: Post-variational rotation angle of the ADT transformation from the block-diagonalization to the final partial diagonalization of the Hamiltonian $(2\times2)$-submatrix.