发表机构
Joint Center for Quantum Information and Computer Science, University of Maryland; Department of Computer Science, University of Maryland; Joint Quantum Institute, NIST/University of Maryland（量子信息与计算机科学联合中心，马里兰大学; 计算机科学系，马里兰大学; 联合量子研究所，美国国家标准与技术研究院/马里兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种仅用单个可测量量子比特，通过鲁棒SWAP门和并行架构，在海森堡极限下学习多体哈密顿量所有参数的方法，实现可扩展的局域测量学习。
AI 中文摘要
哈密顿量学习为重建未知量子动力学提供了一个系统性框架。然而，现有协议通常假设可以直接测量整个系统。借助快速单量子比特控制和连通的参考骨干，我们证明单个可测量的量子比特足以在海森堡极限下学习N个量子比特上有界度二体哈密顿量的所有O(N)个独立参数。关键的是，我们的协议使用由量子信号处理合成的鲁棒SWAP门，使得在遥远哈密顿参数下演化的态能够相干地转移到可测量的量子比特上。这种转移不需要对中间链路的哈密顿参数进行预先校准。一种并行学习架构在N量子比特链上实现了总查询时间O~(N)，同时保持海森堡极限的精度标度。在链上，这些标度与基本精度和信息传播下界匹配，仅相差对数因子。该框架进一步扩展到任意有界度的相互作用图。我们的结果确立了通过仅一个局域测量接口学习大量多体哈密顿参数的可扩展路径。
英文摘要
Hamiltonian learning provides a systematic framework for reconstructing unknown quantum dynamics. However, existing protocols typically assume direct measurement access to the entire system. With fast single-qubit control and a connected reference backbone, we show that a single measurable qubit suffices to learn all $O(N)$ independent parameters of a bounded-degree two-body Hamiltonian on $N$ qubits at the Heisenberg limit. Crucially, our protocol uses robust SWAP gates synthesized by quantum signal processing, enabling coherent transfer of states evolving under distant Hamiltonian parameters to the measurable qubit. This transfer requires no prior calibration of the Hamiltonian parameters of the intermediate links. A parallel learning architecture achieves total query time $\widetilde{O}(N)$ for an $N$-qubit chain, while retaining Heisenberg-limited precision scaling. On the chain, these scalings match the fundamental precision and information-propagation lower bounds up to logarithmic factors. The framework further extends to arbitrary bounded-degree interaction graphs. Our results establish a scalable route to learning an extensive number of many-body Hamiltonian parameters through only a local measurement interface.
Comments32 pages, including 1 figure and 12 pages of Supplementary Material
