What is the relevance of heating measurements of the motion of trapped ions?
Motional heating of trapped ion motion can affect the fidelity of entangling gates, depending on which particular scheme is used to entangle the ions. There are several protocols (the Cirac-Zoller and Molmer-Sorensen, for example) that depend on an initially pure quantum state, or at least a state where the ions are localized to much less than the optical wavelength (Lamb-Dicke limit). In these cases, heating can give gate errors. There are other schemes (such as the Duan or Garcia-Ripoll) that lessen the dependence on motional coherence..
