  Quantum computers hold promise to enable efficient simulations of the
properties of molecules and materials; however, at present they only permit ab
initio calculations of a few atoms, due to a limited number of qubits. In order
to harness the power of near-term quantum computers for simulations of larger
systems, it is desirable to develop hybrid quantum-classical methods where the
quantum computation is restricted to a small portion of the system. This is of
particular relevance for molecules and solids where an active region requires a
higher level of theoretical accuracy than its environment. Here we present a
quantum embedding theory for the calculation of strongly-correlated electronic
states of active regions, with the rest of the system described within density
functional theory. We demonstrate the accuracy and effectiveness of the
approach by investigating several defect quantum bits in semiconductors that
are of great interest for quantum information technologies. We perform
calculations on quantum computers and show that they yield results in agreement
with those obtained with exact diagonalization on classical architectures,
paving the way to simulations of realistic materials on near-term quantum
computers.
