  We present a use case of practical utility of quantum computing by employing
a quantum computer in the investigation of the linear H$_4$ molecule as a
simple model to comply with the requirements of singlet fission. We leverage a
series of independent strategies to bring down the overall cost of the quantum
computations, namely 1) tapering off qubits in order to reduce the size of the
relevant Hilbert space; 2) measurement optimization via rotations to eigenbases
shared by groups of qubit-wise commuting (QWC) Pauli strings; 3) parallel
execution of multiple state preparation + measurement operations, implementing
quantum circuits onto all 20 qubits available in the Quantinuum H1-1 quantum
hardware. We report results that satisfy the energetic prerequisites of singlet
fission and which are in excellent agreement with the exact transition energies
(for the chosen one-particle basis), and much superior to classical methods
deemed computationally tractable for singlet fission candidates
