发表机构
Harvard University; Caltech; Oratomic（哈佛大学; 加州理工学院; Oratomic公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对近期模拟量子模拟器缺乏快速任意量子控制的限制，提出在最小访问模型下学习多体哈密顿量，证明在均匀态和计算基两种受限设置下，通用2-局域及特定最近邻哈密顿量参数均可重建，展示了严格约束下学习的可行性。
AI 中文摘要
从动力学中学习多体系统的哈密顿量是量子科学中的核心任务，然而，具有最强可证明保证的算法假设了一定水平的量子控制——快速、任意的单量子比特门与时间演化交错进行，以及在任意基下的测量——这超出了近期模拟量子模拟器的能力。受模拟原子和离子平台的启发，我们在最小访问模型下研究哈密顿量学习。均匀态制备与测量：我们首先考虑这样的设置，即在每次实验中，可以将每个量子比特旋转到相同的状态，进行短时间演化，并在相同基下测量每个量子比特。令人惊讶的是，我们证明对于任意相互作用图上的通用2-局域哈密顿量，所有参数都可以从这样的实验中重建。计算基态制备与测量：然后我们考虑一个类似受限的设置，但态制备和测量仅限于计算基。对于仅具有泡利X/Z相互作用的最近邻哈密顿量（这一类捕获了当代里德伯原子平台），我们证明在一维和二维矩形晶格上，所有参数都可以从这样的实验中重建，直至不可避免的规范自由度。我们的协议引入了新技术，用于求解具有大量参数的复杂多项式系统。综合来看，我们的结果表明，即使在最严格的实验约束下，人们也可以从量子多体系统的动力学中学到很多东西。
英文摘要
Learning the Hamiltonian of a many-body system from its dynamics is a central task in quantum science, yet the algorithms with the strongest provable guarantees assume some level of quantum control--fast, arbitrary single-qubit gates interleaved with time evolution, and measurements in arbitrary bases--that is beyond the capabilities of near-term analog quantum simulators. Motivated by analog atom- and ion-based platforms, we study Hamiltonian learning under minimal access models. Uniform state preparation and measurements: We first consider the setting where in every experiment, one can rotate each qubit to the same state, perform short-time evolution, and measure every qubit in the same basis. Surprisingly, we show that for generic 2-local Hamiltonians on any interaction graph, all of the parameters can be reconstructed from such experiments. Computational basis state preparation and measurements: We then consider a similarly constrained setting, but where state preparation and measurement are restricted to the computational basis. For nearest-neighbor Hamiltonians with only Pauli $X/Z$ interactions, a class which captures contemporary Rydberg atom platforms, we show that over 1D and 2D rectangular lattices, all of the parameters can be reconstructed from such experiments up to unavoidable gauges. Our protocols introduce new techniques for solving structured polynomial systems over an extensive number of parameters. Taken together, our results suggest that one can learn a great deal from the dynamics of quantum many-body systems even under the most stringent experimental constraints.
Comments87 pages, 7 figures
