提出一种仅依赖短时动力学和局部操作的鲁棒高效哈密顿量学习方法，无需先验信息即可学习 Pauli 基稀疏哈密顿量，对噪声具有弹性，为大规模量子系统动力学的系统理解铺路。
摘要：
随着量子技术的快速发展，数字和模拟量子系统的规模都在急剧增加。为了更好地控制和理解量子硬件，一个重要的任务是表征相互作用，即学习哈密顿量，它决定了系统的静态和动态性质。传统的哈密顿量学习方法要么需要昂贵的量子过程层析，要么采用不切实际的假设，例如关于哈密顿量结构的先验信息以及系统的基态或热态。在这项工作中，我们提出了一种鲁棒且高效的哈密顿量学习方法，该方法仅基于温和的假设便规避了这些限制。所提出的方法仅使用短时间动力学和局部操作，即可高效学习在 Pauli 基上稀疏的任意哈密顿量，而无需任何关于哈密顿量的信息，也无需准备任何本征态或热态。该方法具有可扩展的复杂度，且关于量子比特数量的失败概率趋于零。同时，在存在态制备和测量误差的情况下，它表现鲁棒，并对一定量的电路和散粒噪声具有弹性恢复能力。我们对具有随机相互作用强度的横场 Ising 哈密顿量和分子哈密顿量进行了数值测试，两者均具有可变尺寸和手动添加的噪声。所有这些结果验证了该方法的鲁棒性和有效性，为系统理解大型量子系统的动力学铺平了道路。
英文摘要：
With the fast development of quantum technology, the sizes of both digital and analog quantum systems increase drastically. In order to have better control and understanding of the quantum hardware, an important task is to characterize the interaction, i.e., to learn the Hamiltonian, which determines both static and dynamic properties of the system. Conventional Hamiltonian learning methods either require costly process tomography or adopt impractical assumptions, such as prior information on the Hamiltonian structure and the ground or thermal states of the system. In this work, we present a robust and efficient Hamiltonian learning method that circumvents these limitations based only on mild assumptions. The proposed method can efficiently learn any Hamiltonian that is sparse on the Pauli basis using only short-time dynamics and local operations without any information on the Hamiltonian or preparing any eigenstates or thermal states. The method has a scalable complexity and a vanishing failure probability regarding the qubit number. Meanwhile, it performs robustly given the presence of state preparation and measurement errors and resiliently against a certain amount of circuit and shot noise. We numerically test the scaling and the estimation accuracy of the method for transverse field Ising Hamiltonian with random interaction strengths and molecular Hamiltonians, both with varying sizes and manually added noise. All these results verify the robustness and efficacy of the method, paving the way for a systematic understanding of the dynamics of large quantum systems.
Engineering Precise and Robust Effective Hamiltonians
Institute for Quantum Computing（量子计算研究所）；Department of Physics, University of Waterloo（滑铁卢大学物理系）；Department of Chemistry, University of Waterloo（滑铁卢大学化学系）
Optimal and Robust In-situ Quantum Hamiltonian Learning through Parallelization
Joint Center for Quantum Information and Computer Science, University of Maryland（量子信息与计算机科学联合中心，马里兰大学）；Department of Computer Science, University of Maryland（马里兰大学计算机科学系）；Department of Computer Science, University of California, Santa Barbara（加州大学圣塔芭芭拉分校计算机科学系）；Google Quantum AI（谷歌量子人工智能）
The Quantum Polariton Hamiltonian that Reproduces the Same Mean Acceleration High-Harmonic Generation Spectra as the Classical Hamiltonian in Strong Laser Fields
Inverse designed Hamiltonians for perfect state transfer and remote entanglement generation, and applications in superconducting qubits
University of Science and Technology of China（中国科学技术大学）；Suzhou Institute for Advanced Research, University of Science and Technology of China（中国科学技术大学苏州高等研究院）；Hefei National Laboratory, University of Science and Technology of China（中国科学技术大学合肥国家实验室）；Origin Quantum（本源量子）
Ansatz-free Hamiltonian learning with Heisenberg-limited scaling
Department of Physics, Harvard University, Cambridge, MA 02138, USA（哈佛大学物理系）；Institute for Quantum Information and Matter, California Institute of Technology, CA 91125, USA（加州理工学院量子信息与物质研究所）；School of Engineering and Applied Sciences, Harvard University, Allston, Massachusetts 02134, USA（哈佛大学工程与应用科学学院）；Center for Quantum Information, IIIS, Tsinghua University, Beijing, China（清华大学信息中心）；Department of Mathematics, Duke University, Durham, NC 27708, USA（杜克大学数学系）；Department of Electrical and Computer Engineering, Duke University, Durham, NC 27708, USA（杜克大学电气与计算机工程系）；Duke Quantum Center, Duke University, Durham, NC 27701, USA（杜克大学量子中心）；Department of Computer Science, Virginia Tech, Alexandria, VA 22314, USA（弗吉尼亚理工大学计算机科学系）；Phasecraft Inc., Washington DC, USA（Phasecraft公司）
