  We propose a scheme to realize scalable quantum computation in a planar ion
crystal confined by a Paul trap. We show that the inevitable in-plane
micromotion affects the gate design via three separate effects: renormalization
of the equilibrium positions, coupling to the transverse motional modes, and
amplitude modulation in the addressing beam. We demonstrate that all of these
effects can be taken into account and high-fidelity gates are possible in the
presence of micromotion. This proposal opens the prospect to realize
large-scale fault-tolerant quantum computation within a single Paul trap.
