Wu Ya-Dong, Zhu Yan, Wang Yuexuan, Chiribella Giulio
John Hopcroft Center for Computer Science, Shanghai Jiao Tong University, Shanghai, China.
QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong.
Nat Commun. 2024 Oct 11;15(1):8796. doi: 10.1038/s41467-024-53101-y.
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.
表征多体量子系统对于量子计算和多体物理至关重要。然而，当系统规模较大且感兴趣的属性涉及大量粒子之间的关联时，该问题就变得具有挑战性。在此，我们引入一种神经网络模型，该模型仅使用来自少数相邻位点的测量数据，就能预测具有恒定关联长度的多体量子态的各种量子属性。该模型基于多任务学习技术，我们证明它比传统的单任务方法具有多个优势。通过数值实验，我们表明多任务学习可应用于足够规则的状态，以从短程关联的观测中预测全局属性，如弦序参量，并区分单任务网络无法区分的量子相。值得注意的是，我们的模型似乎能够将从低维量子系统学到的信息转移到高维系统，并对训练中未出现的哈密顿量做出准确预测。
