Rare Earth Ions Doped Mixed Crystals for Fast Quantum Computers with Optical Frequency Qubits

The possibility of using mixed crystals highly doped with rare earth ions (REIs) as physical systems for creating fast quantum computers with a sampling time of nanoseconds is discussed. The electronic 4f states of rare earth ions with small values of the diagonal elements of the Judd-Ofelt matrix U(2) are proposed as optical frequency qubit levels. CNOT and other conditional gate operations are performed by exciting the rare earth ion into the 4f state with a large diagonal element of U(2), causing a Stark blockade. It is found that the main interaction responsible for this blockade is the quadrupole-quadrupole interaction. The large inhomogeneous broadening of the frequencies of the electronic transitions in mixed crystals and the weak interaction of 4f electrons with phonons make it possible to achieve a high computation rate and a long decoherence time of the qubits. An ensemble of closest REIs is described that can act as an OQC instance; the frequencies of the corresponding qubits can be found using the spectral hole burning method.