Effects of ground-state hyperfine shifts in quantum computing with rare-earth-metal ions in solids

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 analyze 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.