  Linear ion trap chains are a promising platform for quantum computation and
simulation. The XY model with long-range interactions can be implemented with a
single side-band Molmer-Sorensen scheme, giving interactions that decay as
$1/r^\alpha$, where $\alpha$ parameterises the interaction range. Lower
$\alpha$ leads to longer range interactions, allowing faster long-range gate
operations for quantum computing. However, decreasing $\alpha$ causes an
increased generation of coherent phonons and appears to dephase the effective
XY interaction model. We characterise and show how to correct for this effect
completely, allowing lower $\alpha$ interactions to be coherently implemented.
Ion trap chains are thus shown to be a viable platform for spatial quantum
search in optimal $O(\sqrt{N})$ time, for $N$ ions. Finally, we introduce a
$O(\sqrt{N})$ quantum state transfer protocol, with a qubit encoding that
maintains a high fidelity.

Quantum Physics