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We propose a scalable design of entangling quantum gates for large ioncrystals with the following desirable features: 1) The gate design is universaland applicable for large ion crystals of arbitrary sizes; 2) The gate has nospeed limitation and can work outside of the Lamb-Dicke region; 3) The gateoperates by driving from either continuous-wave or pulsed laser beams; 4) Thegate is insensitive to slow variation of the laser optical phase and worksunder a thermal state for the ions' motion; 5) The intrinsic gate infidelitycan be reduced to a level well below the threshold for fault-tolerant quantumcomputation under realistic experimental parameters. Different from theprevious gate schemes, here we propose a gate design based on driving of thelocal oscillation mode of the ions instead of the collective normal modes anddevelop a formalism based on the Heisenberg equations to deal with themany-body quantum dynamics outside of the Lamb-Dicke region.

Robust gate design for large ion crystals through excitation of local phonon modes