  We propose a scheme to implement arbitrary-speed quantum entangling gates on
two trapped ions immersed in a large linear crystal of ions, with minimal
control of laser beams. For gate speeds slower than the oscillation frequencies
in the trap, a single appropriately-detuned laser pulse is sufficient for
high-fidelity gates. For gate speeds comparable to or faster than the local ion
oscillation frequency, we discover a five-pulse protocol that exploits only the
local phonon modes. This points to a method for efficiently scaling the ion
trap quantum computer without shuttling ions.
