Characterizing the properties of multiparticle quantum systems is a crucial task for quantum computing and many-body quantum physics. The task, however, becomes extremely challenging when the system size becomes large and when the properties of interest involve global measurements on a large number of sites. Here we develop a multi-task neural network model that can accurately predict global properties of many-body quantum systems, like string order parameters and many-body topological invariants, using only limited measurement data gathered from few neighbouring sites. The model can simultaneously predict multiple quantum properties, including not only expectation values of quantum observables, but also general nonlinear functions of the quantum state, such as entanglement entropies. Remarkably, we find that multi-task training over a given set of quantum properties enables our model to discover new properties outside the original set. Without any labeled data, the model can perform unsupervised classification of quantum phases of matter and uncover unknown boundaries between different phases.

翻译：表征多粒子量子系统的特性是量子计算和多体量子物理学中的关键任务。然而，当系统规模变大，且目标特性涉及对大量位点进行全局测量时，这项任务变得极具挑战性。本文开发了一种多任务神经网络模型，该模型仅利用从少数相邻位点收集的有限测量数据，即可准确预测多体量子系统的全局特性，如弦序参量和多体拓扑不变量。该模型能同时预测多个量子特性，不仅包括量子观测量的期望值，还包括量子态的一般非线性函数，例如纠缠熵。值得注意的是，我们发现，对给定的一组量子特性进行多任务训练，使我们的模型能够发现原始集合之外的新特性。在没有任何标注数据的情况下，该模型可以对物质的量子相进行无监督分类，并发现不同相之间的未知边界。