  The computation of excited electronic states is an important application for
quantum computers. In this work, we simulate the excited state spectra of four
aromatic heterocycles on IBM superconducting quantum computers, focusing on
active spaces of $\pi \to \pi^*$ and $n \to \pi^*$ excitations. We approximate
the ground state with the entanglement forging method, a qubit reduction
technique that maps a spatial orbital to a single qubit, rather than two
qubits. We then determine excited states using the quantum subspace expansion
method. We showcase these algorithms on quantum hardware using up to 8 qubits
and employing readout and gate error mitigation techniques. Our results
demonstrate a successful application of quantum computing in the simulation of
active-space electronic wavefunctions of substituted aromatic heterocycles, and
outline challenges to be overcome in elucidating the optical properties of
organic molecules with hybrid quantum-classical algorithms.
