  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.
