Errors in trapped-ion quantum gates due to spontaneous photon scattering

We analyze the error in trapped-ion, hyperfine qubit, quantum gates due to spontaneous scattering of photons from the gate laser beams. We investigate single-qubit rotations that are based on stimulated Raman transitions and two-qubit entangling phase-gates that are based on spin-dependent optical dipole forces. This error is compared between different ion species currently being investigated as possible quantum information carriers. For both gate types we show that with realistic laser powers the scattering error can be reduced to below current estimates of the fault-tolerance error threshold.