Deep neural networks are a powerful tool for predicting properties of quantum states from limited measurement data. Here we develop a network model that can simultaneously predict multiple quantum properties, including not only expectation values of quantum observables, but also general nonlinear functions of the quantum state, like entanglement entropies and many-body topological invariants. Remarkably, we find that a model trained on a given set of properties can also discover new properties outside that set. Multi-purpose training also enables the model to infer global properties of many-body quantum systems from local measurements, to classify symmetry protected topological phases of matter, and to discover unknown boundaries between different phases.

翻译：深度神经网络是从有限测量数据预测量子态特性的强大工具。本文开发了一种可同时预测多种量子特性的网络模型，不仅能预测量子可观测量的期望值，还能预测量子态的一般非线性函数（如纠缠熵和多体拓扑不变量）。值得注意的是，我们发现基于特定特性集训练的模型还可以发现该集合之外的新特性。多目标训练使模型能够从局部测量推断多体量子系统的全局特性，对对称性保护的拓扑物质相进行分类，并发现不同相之间的未知边界。