发表机构
Department of EECS, UC Berkeley; Google Quantum AI（加州大学伯克利分校电气工程和计算机科学系; 谷歌量子人工智能）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出平稳性检验框架，通过测量局域可观测量的变化率，从热态样本中学习量子多体系统的相互作用图与哈密顿量系数，并改进热亚稳态面积律，算法严格且接近样本最优。
AI 中文摘要
从量子系统的热态（或称“吉布斯态”）样本中学习支配该系统的哈密顿量相互作用，是量子学习理论与多体物理交叉领域的一个基础性问题。在本文中，我们与量子吉布斯采样文献建立联系，引入一种自然的学习算法，称之为平稳性检验：该算法简单地“猜测”哈密顿量，并在相关的细致平衡量子马尔可夫链[CKG23]下测量局域可观测量的变化率。我们利用平稳性检验来解决以下应用：1. 首次给出在所有温度下，给定格点哈密顿量吉布斯态副本时，学习其底层相互作用图（即结构学习）的学习算法。2. 首次给出仅给定热亚稳态（建模为自由能的“局部最小值”）副本时，学习格点哈密顿量系数的学习算法。3. 此外，我们对热亚稳态的近期面积律[BCV25]进行了改进，该面积律在热力学极限下成立。我们的学习算法是严格的、时间高效的，并且在系统规模和精度上接近样本最优。在技术层面，我们的论证基于这些吉布斯采样算法的量子Fisher信息的新的近似局域性和凸性性质。
英文摘要
The task of learning the Hamiltonian interactions governing a quantum system, given samples of its thermal (or 'Gibbs') states, is a foundational question at the intersection of quantum learning theory and many-body physics. In this paper, we draw connections to the quantum Gibbs sampling literature to introduce a natural learning algorithm we call the stationarity test: which simply "guesses" the Hamiltonian, and measures the rate-of-change of local observables, under the associated detailed-balanced quantum Markov chain [CKG23]. We leverage the stationarity test to address the following applications: 1. To give the first learning algorithm for the underlying interaction graph, i.e. structure learning, of lattice Hamiltonians at all temperatures, given copies of their Gibbs states. 2. To give the first learning algorithm for the coefficients of a lattice Hamiltonian, given only copies of its thermal metastable states, modeled as the "local minima" of the free energy. 3. In addition, we present a refinement to the recent area law for thermal metastable states [BCV25], which holds in the thermodynamic limit. Our learning algorithms are rigorous, time-efficient, and nearly sample-optimal in system size and accuracy. At a technical level, our arguments are based on new approximate locality and convexity properties for the quantum Fisher information of these Gibbs sampling algorithms.
Comments62 pages, 4 figures
