$\Delta$ADAPT-VQE: Toward Accurate Calculation of Excitation Energies on Quantum Computers for BODIPY Molecules With Application in Photodynamic Therapy

Quantum chemistry simulations offer a cost-effective way for computational design of BODIPY photosensitizers with potential use in photodynamic therapy (PDT). However, accurate predictions of photophysical properties, such as excitation energies, pose a challenge for the popular time-dependent density functional theory (TDDFT) and equation-of-motion coupled cluster with singles and doubles (EOM-CCSD) methods. By contrast, reliable descriptions can be achieved by multi-reference quantum chemistry methods, though unfortunately, their computational cost grows exponentially with the number of correlated electrons. Alternatively, quantum computing holds a great potential for exact simulation of photophysical properties in a computationally more efficient way. To this end, we introduce the state-specific $\Delta$UCCSD-VQE (unitary coupled cluster with singles and doubles variational quantum eigensolver) and $\Delta$ADAPT-VQE methods in which the electronically excited state is calculated via a non-Aufbau electronic configuration. The accuracy and capability of the developed methods are assessed against experimentally determined excitation energies for six BODIPY-derivatives. We show that the proposed methods predict accurate vertical excitation energies that are not only in good agreement with experimental reference data but also outperform popular quantum chemistry methods, such as TDDFT and EOM-CCSD. Spurred by its impressive performance and simplicity, we are confident that $\Delta$ADAPT will emerge as the method of choice for guiding the rational design of photosensitizers for PDT and photocatalysis in the era of near-term quantum computing.