Characterizing multipartite quantum systems is crucial for quantum computing and many-body physics. The problem, however, becomes challenging when the system size is large and the properties of interest involve correlations among a large number of particles. Here we introduce a neural network model that can predict various quantum properties of many-body quantum states with constant correlation length, using only measurement data from a small number of neighboring sites. The model is based on the technique of multi-task learning, which we show to offer several advantages over traditional single-task approaches. Through numerical experiments, we show that multi-task learning can be applied to sufficiently regular states to predict global properties, like string order parameters, from the observation of short-range correlations, and to distinguish between quantum phases that cannot be distinguished by single-task networks. Remarkably, our model appears to be able to transfer information learnt from lower dimensional quantum systems to higher dimensional ones, and to make accurate predictions for Hamiltonians that were not seen in the training.

翻译：表征多体量子系统对量子计算及多体物理学至关重要。然而，当系统规模庞大且目标性质涉及大量粒子间的关联时，这一问题变得极具挑战性。本文提出一种神经网络模型，该模型仅需利用少数相邻位点的测量数据，即可预测具有恒定关联长度的多体量子态的各种量子性质。该模型基于多任务学习技术，我们证明相较于传统单任务方法，该技术具有多项优势。通过数值实验表明，多任务学习可应用于足够正则的量子态，通过观测短程关联预测全局性质（如弦序参量），并能区分单任务网络无法区分的量子相。值得注意的是，该模型展现出将低维量子系统学习到的信息迁移至更高维系统的能力，且能对训练中未曾见过的哈密顿量做出准确预测。