Errors in stimulated-Raman-induced logic gates in $^{133}$Ba$^+$

${}^{133}\mathrm{Ba}^+$ is illuminated by a laser that is far-detuned from optical transitions, and the resulting spontaneous Raman scattering rate is measured. The observed scattering rate is lower than previous theoretical estimates. The majority of the discrepancy is explained by a more accurate treatment of the scattered photon density of states. This work establishes that, contrary to previous models, there is no fundamental limit to laser-driven quantum gates from laser-induced spontaneous Raman scattering.