Microscopically understanding and classifying phases of matter is at the heart of strongly-correlated quantum physics. With quantum simulations, genuine projective measurements (snapshots) of the many-body state can be taken, which include the full information of correlations in the system. The rise of deep neural networks has made it possible to routinely solve abstract processing and classification tasks of large datasets, which can act as a guiding hand for quantum data analysis. However, though proven to be successful in differentiating between different phases of matter, conventional neural networks mostly lack interpretability on a physical footing. Here, we combine confusion learning with correlation convolutional neural networks, which yields fully interpretable phase detection in terms of correlation functions. In particular, we study thermodynamic properties of the 2D Heisenberg model, whereby the trained network is shown to pick up qualitative changes in the snapshots above and below a characteristic temperature where magnetic correlations become significantly long-range. We identify the full counting statistics of nearest neighbor spin correlations as the most important quantity for the decision process of the neural network, which go beyond averages of local observables. With access to the fluctuations of second-order correlations -- which indirectly include contributions from higher order, long-range correlations -- the network is able to detect changes of the specific heat and spin susceptibility, the latter being in analogy to magnetic properties of the pseudogap phase in high-temperature superconductors. By combining the confusion learning scheme with transformer neural networks, our work opens new directions in interpretable quantum image processing being sensible to long-range order.

翻译：微观理解和分类物质相是强关联量子物理的核心。通过量子模拟，可以获得多体态的真实投影测量（快照），其中包含系统中关联的全部信息。深度神经网络的兴起使得大规模数据集的抽象处理与分类任务变得常规化，这为量子数据分析提供了指导性工具。然而，尽管传统神经网络在区分不同物质相方面已被证明有效，但大多数缺乏基于物理的可解释性。在此，我们将混淆学习与关联卷积神经网络相结合，实现了基于关联函数的完全可解释相检测。具体而言，我们研究了二维海森堡模型的热力学性质，结果表明经过训练的网络能够捕捉到特征温度上下（即磁关联开始显著长程化）快照中的定性变化。我们识别出近邻自旋关联的全计数统计量是神经网络决策过程中最重要的量，这超越了局部观测量的平均值。通过获取二阶关联的涨落（间接包含高阶长程关联的贡献），网络能够检测比热和自旋磁化率的变化，后者类似于高温超导体赝能隙相的磁性质。通过将混淆学习方案与Transformer神经网络相结合，我们的工作为对长程有序敏感的可解释量子图像处理开辟了新方向。