  Quantum chemistry simulations that accurately predict the properties of
materials are among the most highly anticipated applications of quantum
computing. It is widely believed that simulations running on quantum computers
will allow for higher accuracy, but there has not yet been a convincing
demonstration that quantum methods are competitive with existing classical
methods at scale. Here we apply the iterative qubit coupled cluster (iQCC)
method on classical hardware to the calculation of the $T_1 \to S_0$ transition
energies in nine phosphorescent iridium complexes, to determine if quantum
simulations have any advantage over traditional computing methods.
Phosphorescent iridium complexes are integral to the widespread
commercialization of organic light-emitting diode (OLED) technology, yet
accurate computational prediction of their emission energies remains a
challenge. Our simulations would require a gate-based quantum computer with a
minimum of 72 fully-connected and error-corrected logical qubits. Since such
devices do not yet exist, we demonstrate the iQCC quantum method using a
special purpose quantum simulator on classical hardware. The results are
compared to a selection of common density-functional theory (DFT) functionals
(B3LYP, CAM-B3LYP, LC-wHPBE), ab initio methods (HF and MP2), and experimental
data. The iQCC quantum method is found to match the accuracy of the fine-tuned
DFT functionals, has a better Pearson correlation coefficient, and still has
considerable potential for systematic improvement. Based on these results, we
anticipate that the iQCC quantum method will have the required accuracy to
design organometallic complexes when deployed on emerging quantum hardware.
