arXiv 1808.061242018-08-18quant-ph

一维离子链中二维矩形晶格的动力学哈密顿工程

Dynamic Hamiltonian engineering of 2D rectangular lattices in a one-dimensional ion chain

Fereshteh Rajabi, Sainath Motlakunta, Chung-You Shih, Nikhil Kotibhaskar, Qudsia Quraishi, Ashok Ajoy, Rajibul Islam

备注：: 14 pages, 9 figures, 2 tables

摘要：

在量子模拟器中控制自旋或量子位之间的相互作用图允许用户控制的本机相互作用的定制以实现目标哈密尔顿算子。在囚禁离子量子模拟器中设计远程声子介导的自旋-自旋相互作用的灵活性提供了这样的可能性。被困离子是模拟计算困难的量子多体动力学的主要候选者，最容易被困在线性1D链中，限制了它们用于容易地模拟高维自旋模型的实用性。在这项工作中，我们介绍了一种模拟-数字模拟的混合方法，用于模拟2D自旋模型和动态变化的相互作用，以实现一个新的图形使用线性1D链。该方法依赖于通过连续应用斯塔克位移梯度脉冲的时域哈密顿算子工程，并且其中脉冲序列可以简单地从目标哈密顿算子在晶格耦合空间上的傅立叶级数分解获得。我们专注于工程二维矩形最近邻自旋晶格，证明所需的控制参数与离子数呈线性关系。这种混合的方法提供了令人信服的可能性，使用1D链的研究中的哈密顿猝灭，动态相变，量子运输在2D和3D。我们讨论了一个可能的实验实现这种方法使用真正的实验参数。

英文摘要：

Controlling the interaction graph between spins or qubits in a quantum simulator allows user-controlled tailoring of native interactions to achieve a target Hamiltonian. The flexibility of engineering long-ranged phonon-mediated spin-spin interactions in a trapped ion quantum simulator offers such a possibility. Trapped ions, a leading candidate for simulating computationally hard quantum many-body dynamics, are most readily trapped in a linear 1D chain, limiting their utility for readily simulating higher dimensional spin models. In this work, we introduce a hybrid method of analog-digital simulation for simulating 2D spin models and dynamically changing interactions to achieve a new graph using a linear 1D chain. The method relies on time domain Hamiltonian engineering through a successive application of Stark shift gradient pulses, and wherein the pulse sequence can simply be obtained from a Fourier series decomposition of the target Hamiltonian over the space of lattice couplings. We focus on engineering 2D rectangular nearest-neighbor spin lattices, demonstrating that the required control parameters scale linearly with ion number. This hybrid approach offers compelling possibilities for the use of 1D chains in the study of Hamiltonian quenches, dynamical phase transitions, and quantum transport in 2D and 3D. We discuss a possible experimental implementation of this approach using real experimental parameters.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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