  Using a recently developed quantum embedding theory, we present first
principles calculations of strongly correlated states of spin defects in
diamond. Within this theory, effective Hamiltonians are constructed, which can
be solved by classical and quantum computers; the latter promise a much more
favorable scaling as a function of system size than the former. In particular,
we report a study of the neutral group-IV vacancy complexes in diamond, and we
discuss their strongly-correlated spin-singlet and spin-triplet excited states.
Our results provide valuable predictions for experiments aimed at optical
manipulation of these defects for quantum information technology applications.
