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

Abstract

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 Mølmer–Sørensen scheme, giving interactions that decay as , where parameterises the interaction range. Lower leads to longer range interactions, allowing faster long-range gate operations for quantum computing. However, decreasing 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 interactions to be coherently implemented. Ion trap chains are thus shown to be a viable platform for spatial quantum search in optimal time, for N ions. Finally, we introduce a quantum state transfer protocol, with a qubit encoding that maintains a high fidelity.