  We explore the simulation of conical intersections (CIs) on quantum devices,
setting the groundwork for potential applications in nonadiabatic quantum
dynamics within molecular systems. The intersecting potential energy surfaces
of H$_{3}^{+}$ are computed from a variance-based contracted quantum
eigensolver. We show how the CIs can be correctly described on quantum devices
using wavefunctions generated by the anti-Hermitian contracted Schr{\"o}dinger
equation ansatz, which is a unitary transformation of wavefunctions that
preserves the topography of CIs. A hybrid quantum-classical procedure is used
to locate the seam of CIs. Additionally, we discuss the quantum implementation
of the adiabatic to diabatic transformation and its relation to the geometric
phase effect. Results on noisy intermediate-scale quantum devices showcase the
potential of quantum computers in dealing with problems in nonadiabatic
chemistry.
