  We developed a general framework for hybrid quantum-classical computing of
molecular and periodic embedding approaches based on an orbital space
separation of the fragment and environment degrees of freedom. We demonstrate
its potential by presenting a specific implementation of periodic
range-separated DFT coupled to a quantum circuit ansatz, whereby the
variational quantum eigensolver and the quantum equation-of-motion algorithm
are used to obtain the low-lying spectrum of the embedded fragment Hamiltonian.
Application of this scheme to study localized electronic states in materials is
showcased through the accurate prediction of the optical properties of the
neutral oxygen vacancy in magnesium oxide (MgO). Despite some discrepancies in
the position of the main absorption band, the method demonstrates competitive
performance compared to state-of-the-art ab initio approaches, particularly
evidenced by the excellent agreement with the experimental photoluminescence
emission peak.
