Understanding the dynamics of large quantum systems is hindered by the curse of dimensionality. Statistical learning offers new possibilities in this regime by neural-network protocols and classical shadows, while both methods have limitations: the former is plagued by the predictive uncertainty and the latter lacks the generalization ability. Here we propose a data-centric learning paradigm combining the strength of these two approaches to facilitate diverse quantum system learning (QSL) tasks. Particularly, our paradigm utilizes classical shadows along with other easily obtainable information of quantum systems to create the training dataset, which is then learnt by neural networks to unveil the underlying mapping rule of the explored QSL problem. Capitalizing on the generalization power of neural networks, this paradigm can be trained offline and excel at predicting previously unseen systems at the inference stage, even with few state copies. Besides, it inherits the characteristic of classical shadows, enabling memory-efficient storage and faithful prediction. These features underscore the immense potential of the proposed data-centric approach in discovering novel and large-scale quantum systems. For concreteness, we present the instantiation of our paradigm in quantum state tomography and direct fidelity estimation tasks and conduct numerical analysis up to 60 qubits. Our work showcases the profound prospects of data-centric artificial intelligence to advance QSL in a faithful and generalizable manner.

翻译：理解大型量子系统的动力学受困于维度灾难。统计学习通过神经网络协议和经典阴影在该领域中提供了新的可能性，但这两种方法均存在局限性：前者受预测不确定性的困扰，后者缺乏泛化能力。本文提出了一种结合这两类方法优势的数据中心学习范式，以促进多样化的量子系统学习任务。具体而言，该范式利用经典阴影以及量子系统的其他易获取信息构建训练数据集，随后由神经网络学习以揭示所探索量子系统学习问题的潜在映射规则。借助神经网络的泛化能力，该范式可离线训练，并在推理阶段（即使只有少量状态副本）对未见过的新系统进行卓越预测。此外，该范式继承了经典阴影的特性，能实现内存高效存储与可靠预测。这些特性凸显了所提出的数据中心方法在发现新型及大规模量子系统方面的巨大潜力。我们具体将该范式实例化于量子态层析和直接保真度估计任务中，并进行了多达60量子比特的数值分析。本研究展示了数据中心人工智能在促进量子系统学习实现可靠且可泛化发展的深远前景。