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 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.

arXiv comment17 pages, 10 figures

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• Quantum search in many-body interacting system with long-range interaction
• Exactly solvable dynamics and signatures of integrability in an infinite-range many-body Floquet spin system
• Geodesic Algorithm for Unitary Gate Design with Time-Independent Hamiltonians
• Signatures of Integrability and Exactly Solvable Dynamics in an Infinite-Range Many-Body Floquet Spin System
• Quantum dynamics of frustrated Josephson junction arrays embedded in a transmission line: an effective XX spin chain with long-range interaction
• Exact Solvability Of Entanglement For Arbitrary Initial State in an Infinite-Range Floquet System
• Persistence of the Berezinskii-Kosterlitz-Thouless transition with long-range couplings
• Revealing effects of local dimension on variable-range interacting model by connecting Lieb-Robinson bounds and multipartite entanglement
• Bose-Hubbard model with power-law hopping in one dimension