Quantum state tomography (QST) is an indispensable tool for characterizing many-body quantum systems. However, due to the exponential scaling of the cost of the protocol with system size, many approaches have been developed for quantum states with specific structure, such as low-rank states. In this paper, we show how approximate message passing (AMP), an algorithmic framework for sparse signal recovery, can be used to perform low-rank QST. AMP provides asymptotically optimal performance guarantees for large sparse recovery problems, which suggests its utility for QST. We discuss the design challenges that come with applying AMP to QST, and show that by properly designing the AMP algorithm, we can reduce the reconstruction error by over an order of magnitude compared to existing approaches to low-rank QST. We also performed tomographic experiments on IBM Kingston and considered the effect of device noise on the reliability of the predicted fidelity of state preparation. Our work advances the state of low-rank QST and may be applicable to other quantum tomography protocols.

翻译：量子态层析（QST）是表征多体量子系统不可或缺的工具。然而，由于该协议的成本随系统规模呈指数级增长，目前已针对具有特定结构的量子态（例如低秩态）发展出多种方法。本文展示了如何利用近似消息传递（AMP）——一种用于稀疏信号恢复的算法框架——来执行低秩量子态层析。AMP为大规模稀疏恢复问题提供了渐近最优的性能保证，这暗示了其在量子态层析中的实用性。我们讨论了将AMP应用于量子态层析所面临的设计挑战，并表明通过合理设计AMP算法，与现有的低秩量子态层析方法相比，我们可以将重构误差降低一个数量级以上。我们还在IBM Kingston上进行了层析实验，并考虑了设备噪声对态制备保真度预测可靠性的影响。我们的工作推进了低秩量子态层析的研究，并可能适用于其他量子层析协议。