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

TL;DR

This paper demonstrates how to implement and correct long-range XY interactions in ion trap chains, enabling efficient quantum state transfer and spatial search with high fidelity, advancing quantum computation capabilities.

Contribution

It introduces a method to coherently implement and correct long-range XY interactions in ion traps, facilitating faster quantum operations and spatial search algorithms.

Findings

Corrected for phonon-induced dephasing effects

Achieved $O( ootN)$ quantum state transfer with high fidelity

Enabled spatial quantum search in $O( ootN)$ time

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 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.