  We propose a scheme to implement quantum gates on any pair of trapped ions
immersed in a large linear crystal, using interaction mediated by the
transverse phonon modes. Compared with the conventional approaches based on the
longitudinal phonon modes, this scheme is much less sensitive to ion heating
and thermal motion outside of the Lamb-Dicke limit thanks to the stronger
confinement in the transverse direction. The cost for such a gain is only a
moderate increase of the laser power to achieve the same gate speed. We also
show how to realize arbitrary-speed quantum gates with transverse phonon modes
based on simple shaping of the laser pulses.
