Abstract Trapped-ion quantum simulators, in analog and digital modes, are considered a primary candidate to achieve quantum advantage in quantum simulation and quantum computation. The underlying controlled ion–laser interactions induce all-to-all two-spin interactions via the collective modes of motion through Cirac–Zoller or Mølmer–Sørensen schemes, leading to effective two-spin Hamiltonians, as well as two-qubit entangling gates. In this work, the Mølmer–Sørensen scheme is extended to induce three-spin interactions via tailored first- and second-order spin–motion couplings. The scheme enables engineering single-, two-, and three-spin interactions, and can be tuned via an enhanced protocol to simulate purely three-spin dynamics. Analytical results for the effective evolution are presented, along with detailed numerical simulations of the full dynamics to support the accuracy and feasibility of the proposed scheme for near-term applications. With a focus on quantum simulation, the advantage of a direct analog implementation of three-spin dynamics is demonstrated via the example of matter-gauge interactions in the U(1) lattice gauge theory within the quantum link model. The mapping of degrees of freedom and strategies for scaling the three-spin scheme to larger systems, are detailed, along with a discussion of the expected outcome of the simulation of the quantum link model given realistic fidelities in the upcoming experiments. The applications of the three-spin scheme go beyond the lattice gauge theory example studied here and include studies of static and dynamical phase diagrams of strongly interacting condensed-matter systems modeled by two- and three-spin Hamiltonians.

中文翻译：

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在捕获离子系统中设计一个有效的三自旋哈密顿量，用于量子模拟

摘要 模拟和数字模式下的俘获离子量子模拟器被认为是在量子模拟和量子计算中实现量子优势的主要候选者。潜在的受控离子-激光相互作用通过 Cirac-Zoller 或 Mølmer-Sørensen 方案的集体运动模式诱导全对全双自旋相互作用，从而产生有效的双自旋哈密顿量以及双量子比特纠缠门。在这项工作中，Mølmer-Sørensen 方案被扩展以通过定制的一阶和二阶自旋运动耦合来诱导三自旋相互作用。该方案支持工程单、二和三自旋相互作用，并且可以通过增强协议进行调整以模拟纯三自旋动力学。给出了有效进化的分析结果，以及完整动力学的详细数值模拟，以支持所提出方案在近期应用中的准确性和可行性。以量子模拟为重点，通过量子链接模型中 U(1) 晶格规范理论中的物质-规范相互作用的示例，证明了三自旋动力学的直接模拟实现的优势。详细介绍了自由度的映射和将三自旋方案扩展到更大系统的策略，并讨论了在即将进行的实验中给出现实保真度的量子链路模型模拟的预期结果。