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：在微观层面理解并分类物质相是强关联量子物理的核心。通过量子模拟，可以获取多体态的真实投影测量（快照），其中包含系统关联的全部信息。深度神经网络的兴起使得常规性地解决大型数据集的抽象处理与分类任务成为可能，这为量子数据分析提供了指导工具。然而，尽管常规神经网络已被证明能有效区分不同物质相，但其大多缺乏基于物理基础的可解释性。本文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伯模型的热力学性质，训练后的网络能捕捉到特征温度上下（该温度下磁关联显著变为长程）快照中的定性变化。我们确定最近邻自旋关联的全计数统计是神经网络决策过程中最重要的量，其超越了局域可观测量平均值的范畴。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——后者与高温超导体赝能隙相的磁性特征类似。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序敏感的可解释量子图像处理开辟了新方向。