  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.
