  Conical intersections (CIs) are pivotal in many photochemical processes.
Traditional quantum chemistry methods, such as the state-average
multi-configurational methods, face computational hurdles in solving the
electronic Schr\"odinger equation within the active space on classical
computers. While quantum computing offers a potential solution, its feasibility
in studying CIs, particularly on real quantum hardware, remains largely
unexplored. Here, we present the first successful realization of a hybrid
quantum-classical state-average complete active space self-consistent field
method based on the variational quantum eigensolver (VQE-SA-CASSCF) on a
superconducting quantum processor. This approach is applied to investigate CIs
in two prototypical systems - ethylene (C2H4) and triatomic hydrogen (H3). We
illustrate that VQE-SA-CASSCF, coupled with ongoing hardware and algorithmic
enhancements, can lead to a correct description of CIs on existing quantum
devices. These results lay the groundwork for exploring the potential of
quantum computing to study CIs in more complex systems in the future.
