Quantum computing with an inhomogeneously broadened ensemble of ions: Suppression of errors from detuning variations by specially adapted pulses and coherent population trapping

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 +/-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.