2022

Ion Trap Long-Range XY Model for Quantum State Transfer and Optimal Spatial Search

Dylan Lewis, Leonardo Banchi, Yi Hong Teoh, Rajibul Islam, and Sougato Bose.

**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 1/rα
, where α parameterises the interaction range. Lower
α leads to longer range interactions, allowing faster long-range gate operations for quantum computing. However, decreasing α 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 α interactions to be coherently implemented. Ion trap chains are thus
shown to be a viable platform for spatial quantum search in optimal O(√N) time, for N ions. Finally, we introduce a O(√N) quantum state transfer protocol, with a qubit encoding that maintains a high fidelity