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

• URL: http://arxiv.org/abs/2206.13685v1
• Date: Tue, 28 Jun 2022 01:28:51 GMT
• Title: Ion Trap Long-Range XY Model for Quantum State Transfer and Optimal Spatial Search
• Authors: Dylan Lewis, Leonardo Banchi, Yi Hong Teoh, Rajibul Islam, Sougato Bose
• Abstract summary: Linear ion trap chains are a promising platform for quantum computation and simulation. Lower $alpha$ leads to longer range interactions, allowing faster long-range gate operations for quantum computing. We show how to correct for this effect completely, allowing lower $alpha$ interactions to be coherently implemented.
• Score: 0.5249805590164902
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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