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We propose a scheme to implement arbitrary-speed quantum entangling gates ontwo trapped ions immersed in a large linear crystal of ions, with minimalcontrol of laser beams. For gate speeds slower than the oscillation frequenciesin the trap, a single appropriately-detuned laser pulse is sufficient forhigh-fidelity gates. For gate speeds comparable to or faster than the local ionoscillation frequency, we discover a five-pulse protocol that exploits only thelocal phonon modes. This points to a method for efficiently scaling the iontrap quantum computer without shuttling ions.Comment: 4 page

Arbitrary-speed quantum gates within large ion crystals through minimum control of laser beams