Quantum state tomography is a daunting challenge of experimental quantum computing, even in moderate system size. One way to boost the efficiency of state tomography is via local measurements on reduced density matrices, but the reconstruction of the full state thereafter is hard. Here, we present a machine-learning method to recover the ground states of \(k\)-local Hamiltonians from just the local information, where a fully connected neural network is built to fulfill the task with up to seven qubits. In particular, we test the neural network model with a practical dataset, that in a 4-qubit nuclear magnetic resonance system our method yields global states via the 2-local information with high accuracy. Our work paves the way towards scalable state tomography in large quantum systems.

量子状态层析成像是实验量子计算的艰巨挑战，即使在中等系统规模下也是如此。提高状态层析成像效率的一种方法是通过对密度降低的矩阵进行局部测量，但是此后很难重建完整状态。在这里，我们提出了一种机器学习方法，可以仅从本地信息中恢复\（k \）-本地哈密顿量的基态，其中建立了一个完全连接的神经网络，以最多7个量子位来完成任务。特别是，我们用一个实际的数据集测试了神经网络模型，即在4量子位核磁共振系统中，我们的方法可以通过2局部信息以高精度生成全局状态。我们的工作为大型量子系统中的可伸缩状态层析成像铺平了道路。