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arXiv 2108.01022quant-phcond-mat.quant-gashep-latnucl-th
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囚禁离子系统中有效三自旋哈密顿量的设计及其在量子模拟中的应用

Engineering an Effective Three-spin Hamiltonian in Trapped-ion Systems for Applications in Quantum Simulation

Bárbara Andrade, Zohreh Davoudi, Tobias Graß, Mohammad Hafezi, Guido Pagano, Alireza Seif

摘要:

在量子模拟和量子计算中,模拟和数字模式的囚禁离子量子模拟器被认为是实现量子优势的主要候选者。受控离子与激光的相互作用通过Cirac-Zoller或Molmer-Sorensen方案的集体运动模式诱导了全对全的双自旋相互作用,从而产生了有效的双自旋哈密顿量和双量子比特纠缠门。在这项工作中,Molmer-Sorensen计划扩展到诱导三自旋相互作用通过定制的第一和第二阶自旋运动耦合。该方案能够实现单自旋、双自旋和三自旋相互作用,并且可以通过增强的协议进行调整,以模拟纯三自旋动力学。有效的演变的分析结果,以及详细的数值模拟的完整的动态支持的准确性和可行性,所提出的计划,为近期的应用。以量子模拟为重点,通过量子链模型下U(1)格点规范理论中物质-规范相互作用的例子,展示了直接模拟实现三自旋动力学的优势。映射的自由度和战略的规模的三自旋计划,以更大的系统,详细的,随着讨论的预期结果的模拟的量子链路模型在即将到来的实验中给出了现实的可行性。三自旋方案的应用超出了这里研究的格点规范理论的例子,包括研究由两个和三个自旋哈密顿量建模的强相互作用凝聚态系统的静态和动态相图。

英文摘要:

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 Molmer-Sorensen schemes, leading to effective two-spin Hamiltonians, as well as two-qubit entangling gates. In this work, the Molmer-Sorensen 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.

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