Ion trap long-range XY model for quantum state transfer and optimal spatial search

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 M circle divide lmer-S circle divide rensen scheme, giving interactions that decay as 1/r(alpha), where alpha parameterises the interaction range. Lower a 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(root N) time, for N ions. Finally, we introduce a O(root N) quantum state transfer protocol, with a qubit encoding that maintains a high fidelity.