# Quantum computer simulation of near-surface oxygen vacancies in α-Al_{2}O_{3}

## Abstract

We study the technologically relevant α-$Al{_2}O_3$ (0001) surface, which is known to host applications such as catalysis, and naturally occurring processes such as corrosion. Near-surface oxygen vacancies are critical to describe these processes, and in this talk we provide an in-depth analysis of the vacancy defects in α-$Al{_2}O_3$ (0001) surface with density functional theory and quantum computer simulations. Employing first-principles calculations we describe the electronic properties of pristine α-$Al{_2}O_3$ (0001) surface and of near-surface O vacancies. Using a hybrid exchange-correlation functional (HSE06), we first obtain the relaxed pristine (0001) surface with Al termination. These geometries are consistent with X-ray diffraction results. Upon introducing an O vacancy, a highly non-dispersive in-gap electronic defect state appears that was absent for the pristine surface. Its band-decomposed charge density and that of the second unoccupied state reveal a strong charge localization near the O vacancy and the adjacent surface Al atom. Next, we study these vacancy states with quantum defect embedding theory (QDET) calculations to unravel their ground and excited-state properties. We define an active space consisting of strongly localized states near the defect and treat the remainder as environment. An effective Hamiltonian is solved for the active space which includes the effective screening from the environment within the random phase approximation to obtain the eigenvalues with full configurational interaction (FCI). Furthermore, we solve the effective Hamiltonian on a quantum computer by employing a model consisting of an active space of one occupied and one unoccupied band from the QDET calculation. On a four-qubit circuit with a Unitary coupled-cluster (UCC-3) ansatz, we calculate the ground-state energy for the active space with Variational quantum eigensolver (VQE). On a noiseless simulator, we achieve excellent agreement with the reference FCI values. Upon running the calculations on a quantum computer, we obtain an error of 0.28±0.04 eV owing to the noise in the hardware. To mitigate noise, we employed Zero-Noise extrapolation with global folding and successfully reduced the error to 0.09±0.04 eV. *We wish to acknowledge funding by the IBM-Illinois Discovery Accelerator Institute.