Modern day quantum simulators can prepare a wide variety of quantum states but the accurate estimation of observables from tomographic measurement data often poses a challenge. We tackle this problem by developing a quantum state tomography scheme which relies on approximating the probability distribution over the outcomes of an informationally complete measurement in a variational manifold represented by a convolutional neural network. We show an excellent representability of prototypical ground- and steady states with this ansatz using a number of variational parameters that scales polynomially in system size. This compressed representation allows us to reconstruct states with high classical fidelities outperforming standard methods such as maximum likelihood estimation. Furthermore, it achieves a reduction of the estimation error of observables by up to an order of magnitude compared to their direct estimation from experimental data.

现代量子模拟器可以准备各种各样的量子态，但从断层扫描测量数据中准确估计可观测物通常是一个挑战。我们通过开发一种量子态断层扫描方案来解决这个问题，该方案依赖于近似于由卷积神经网络表示的变分流形中信息完整测量结果的概率分布。我们使用许多在系统大小上呈多项式缩放的变分参数，展示了该 ansatz 原型基态和稳态的出色可表示性。这种压缩表示允许我们重建具有高经典保真度的状态，优于标准方法，例如最大似然估计。此外，