  We propose a scalable design of entangling quantum gates for large ion
crystals with the following desirable features: 1) The gate design is universal
and applicable for large ion crystals of arbitrary sizes; 2) The gate has no
speed limitation and can work outside of the Lamb-Dicke region; 3) The gate
operates by driving from either continuous-wave or pulsed laser beams; 4) The
gate is insensitive to slow variation of the laser optical phase and works
under a thermal state for the ions' motion; 5) The intrinsic gate infidelity
can be reduced to a level well below the threshold for fault-tolerant quantum
computation under realistic experimental parameters. Different from the
previous gate schemes, here we propose a gate design based on driving of the
local oscillation mode of the ions instead of the collective normal modes and
develop a formalism based on the Heisenberg equations to deal with the
many-body quantum dynamics outside of the Lamb-Dicke region.

Quantum Physics