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.
@article{arxiv.quant-ph/0508037,
title = {Arbitrary-speed quantum gates within large ion crystals through minimum control of laser beams},
author = {Shi-Liang Zhu and C. Monroe and L. -M. Duan},
journal= {arXiv preprint arXiv:quant-ph/0508037},
year = {2009}
}