Analytical Nonadiabatic Couplings and Gradients within the State-Averaged Orbital-Optimized Variational Quantum Eigensolver

Abstract

We introduce several technical and analytical extensions to our recent state-averaged orbital-optimized variational quantum eigensolver (SA-OO-VQE) algorithm (see Yalouz et al. Quantum Sci. Technol. 2021, 6, 024004). Motivated by the limitations of current quantum computers, the first extension consists of 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 nonadiabatic 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 biomolecules), for which we also perform a geometry optimization to locate a conical intersection between the ground and first-excited electronic states of the molecule.

Quantum algorithms for electronic structures: basis sets and boundary conditions

“…71 This approach was further generalized to correctly describe (near-)degenerate states in avoided crossings or conical intersections by implementing analytical gradient and nonadiabatic couplings. 116,117 Together with the reduced density matrix sampling technique, CASSCF has been applied to a carbon monoxide molecule with a cc-pVDZ basis set to determine the stability of the algorithm in the presence of gate noise, decoherence, and a parameterized quantum circuit for the state. 118…”

Toward density functional theory on quantum computers?

“…More efficient algorithms have therefore been developed such as the quantum stochastic drift protocol [14], or the direct simulation of the Hamiltonian using linear combination of unitaries and the qubitization formalism [15][16][17][18]. More adapted to the NISQ era, several variational quantum algorithms (hybrid quantum-classical) have been specifically designed to prepare ground states [19][20][21][22][23] and, more recently, excited states [24][25][26], and to calculate atomic forces and molecular properties [27][28][29][30].…”

Toward Density Functional Theory on Quantum Computers ?

“…More efficient algorithms have therefore been developed such as the quantum stochastic drift protocol [11], or the direct simulation of the Hamiltonian using linear combination of unitaries and the qubitization formalism [12][13][14][15]. More adapted to the NISQ era, several variational quantum algorithms (hybrid quantumclassical algorithms) have been specifically designed to prepare ground states [16][17][18][19][20] and, more recently, excited states [21][22][23], and to calculate of atomic forces and molecular properties [24][25][26][27].…”