  The proposal for quantum computing with rare-earth-ion qubits in inorganic
crystals makes use of the inhomogeneous broadening of optical transitions in
the ions to associate individual qubits with ions responding to radiation in
selected frequency channels. We show that a class of Gaussian composite pulses
and complex sech pulses provide accurate qubit pi-rotations, which are at the
same time channel selective on a 5 MHz frequency scale and tolerant to 0.5 MHz
deviations of the transition frequency of ions within a single channel.
Rotations in qubit space of arbitrary angles and phases are produced by
sequences of pi-pulses between the excited state of the ions and coherent
superpositions of the qubit states.
