发表机构
Department of Physics and Astronomy, University of Florence; Department of Physics and Astronomy, University College London; Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（物理学与天文学系，佛罗伦萨大学; 物理学与天文学系，伦敦大学学院; 基础与前沿科学研究所，电子科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究如何从有限子系统学习量子拓扑相，引入数据高效的监督学习框架，利用子系统约化密度矩阵构建量子核，通过对两个自旋模型相图分类测试，该方法在少位点操作时相分类精度高且能推广，为表征量子多体系统相图提供实用途径。
AI 中文摘要
表征量子拓扑相需要测量非局域弦序参量，这要求能访问整个系统，而这在实验上通常不可行。在这项工作中，我们引入了一个数据高效的监督学习框架，通过从小子系统识别量子相来规避这一限制。我们的协议利用由这些子系统的约化密度矩阵构建的量子核，它可通过实验有效估计。我们用一维晶格上两个自旋模型（广义团簇伊辛自旋 - 1/2链和各向异性霍尔丹自旋 - 1链）的相图分类对框架进行基准测试。显著的是，当操作限于少至一到四个位点时，我们的方法在相分类中实现了高精度，并且即使在中等系统规模上训练，也能推广到更长的链。这些发现表明局部约化密度矩阵保留了全局拓扑相的关键特征，为表征量子多体系统丰富的相图提供了一条实用途径。
英文摘要
Characterizing quantum topological phases requires measuring non-local string order parameters, demanding access to the full system, which is often experimentally unfeasible. In this work, we introduce a data-efficient supervised learning framework that circumvents this limitation by recognizing quantum phases from small subsystems. Our protocol utilizes a quantum kernel constructed from the reduced density matrices of these subsystems, which can be efficiently estimated experimentally. We benchmark our framework with the classification of the phase diagrams of two spin models on one-dimensional lattices, namely the generalized cluster-Ising spin-1/2 chain and the anisotropic Haldane spin-1 chain. Remarkably, our approach achieves high accuracy in phase classification when operations are limited to as few as one to four sites, and it also generalizes to longer chains even when trained on moderate system sizes. These findings demonstrate that local reduced density matrices preserve vital signatures of global topological phases, offering a practical route to characterize rich phase diagrams of quantum many-body systems.
