  We present an investigation of the effects of constant but random shifts of
the ground hyperfine qubit states in the setting of quantum computing with ion
doped crystals. Complex hyperbolic secant pulses can be used to transfer ions
reliably to electronically excited states, and a perturbative approach is used
to analyse the effect of ground state hyperfine shifts. This analysis shows
that the errors due to the hyperfine shift are dynamically supressed during
gate operation, a fact we attribute to the AC Stark shift. Furthermore we
present an implementation of a controlled phase gate which is resilient to the
effects of the hyperfine shift. Decoherence and decay effects are included in
simulations in order to show that a demonstration of quantum gates is feasible
over the relevant range of system parameters.
