  Two or three dimensional Paul traps can confine a large number of ions
forming a Wigner crystal, which would provide an ideal architecture for
scalable quantum computation except for the micromotion, an issue that is
widely believed to be the killer for high fidelity quantum gates. Surprisingly,
here we show that the micromotion is not an obstacle at all for design of high
fidelity quantum gates, even though the magnitude of the micromotion is
significantly beyond the requirement of the Lamb-Dicke condition. Through exact
solution of the quantum Mathieu equations, we demonstrate the principle of the
gate design under micromotion using two ions in a quadrupole Paul trap as an
example. The proposed micromotion quantum gates can be extended to the many ion
case, paving a new way for scalable trapped ion quantum computation.
