Excited electronic states play an important role in many areas of physics and chemistry and have a large number of technological and materials science applications, for instance, photovoltaics, lighting and photocatalysis, which include such materials as semiconductors, molecular chromophores, carbon nanotubes, to name a few. At the same time, quantum devices improve very rapidly and the question is how to map chemistry problems onto existing quantum hardware. In this work, we demonstrate how the excited state calculations could be carried out on a D-Wave 2000Q quantum annealer. To achieve this goal, the excited states are treated using two methods, time-dependent Hartree-Fock (TDHF) and time-dependent density-functional theory (TDDFT), both within a commonly used Tamm-Dancoff approximation (TDA). Both theories lead to eigenvalue problems which are solved on a quantum annular using the Quantum Annealer Eigensolver (QAE), developed previously. In addition to computing excitation energies, the method is also capable of computing all desirable chemically important properties, such as transition dipole moments and oscillator strengths, as it is shown on a number of small molecular species. Also, we reproduce a typical basis set convergence for H₂ molecule and compute three excitation energies of NH₃ as a function of molecular geometry. All excitation energy errors are less than or about 0.2 eV for the TDDFT+QAE calculations, which is an acceptable accuracy of the TDDFT method in general. In contrast, we find that the TDHF+QAE errors tend to be larger by one or two orders of magnitude.

TDDFT excitation energies for the umbrella inversion of ammonia (NH<sub>3</sub>) for singlet states. The first three excitation energies are computed using the QAE and D-Wave 2000Q quantum annealer (dashed red, green and blue curves). The reference calculation is shown for comparison (thin black curves). The angle is the improper H-N-H-H dihedral angle.

TDDFT excitation energies for the umbrella inversion of ammonia (NH₃) for singlet states. The first three excitation energies are computed using the QAE and D-Wave 2000Q quantum annealer (dashed red, green and blue curves). The reference calculation is shown for comparison (thin black curves). The angle is the improper H-N-H-H dihedral angle.

Susan Mniszewski

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