  The ion trap quantum computer proposed by Cirac and Zoller is analyzed for
decoherence due to vibrations of the ions. An adiabatic approximation
exploiting the vast difference between the frequencies of the optical
intraionic transition and the vibrational modes is used to find the decoherence
time at any temperature T. The scaling of this decoherence time with the number
of ions is discussed, and compared to that due to spontaneous emission.
