The proposal for quantum computing with rare-earth-metal-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 $\pm 0.5\mathrm{MHz}$ 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.

• Received 13 May 2003

DOI:https://doi.org/10.1103/PhysRevA.69.022321