Recent theoretical progress has established conditions under which machine learning models can efficiently predict ground-state properties of gapped local Hamiltonians when trained on quantum-generated data. Previous experimental demonstrations in this paradigm, however, have largely been limited to small systems or highly structured states, due to the difficulty of preparing many-body ground states on quantum processors. In this work, we demonstrate learning from experimental quantum data generated from approximate ground states of the two-dimensional Heisenberg XXZ model with system sizes up to 115 qubits. We construct a dataset of single-site expectation values, two-point correlations, and 12-body loop correlations across the antiferromagnetic phase. We then train neural networks on this data and show that they can accurately predict spatially resolved observables for previously unseen Hamiltonian parameters, both within the training distribution and in an out-of-distribution regime approaching the phase boundary. Our results demonstrate the practical realization of learning from quantum data for an interacting two-dimensional many-body system at scale, motivating a path toward regimes where quantum processors could provide training data beyond the reach of classical approximation methods.

翻译：近期理论进展确立了机器学习模型在基于量子生成数据训练时，能够高效预测有能隙局域哈密顿量基态性质的条件。然而，由于在量子处理器上制备多体基态存在困难，该范式下的先前实验演示主要局限于小规模系统或高度结构化态。本研究演示了从由二维海森堡XXZ模型近似基态生成的实验量子数据中学习，系统尺寸达115量子比特。我们构建了涵盖反铁磁相位中单点期望值、两点关联函数及12体环关联函数的数据集。随后在该数据集上训练神经网络，结果表明网络能准确预测未见哈密顿量参数的空间分辨可观测量——既包含训练分布内区域，也涵盖趋近相边界时分布外区域。我们的结果实现了从量子数据中学习大规模相互作用二维多体系统的实践可能，为推进至量子处理器能提供超越经典近似方法训练数据的参数区域指明了路径。