Quantum state tomography is a powerful, but resource-intensive, general solution for numerous quantum information processing tasks. This motivates the design of robust tomography procedures that use relevant resources as sparingly as possible. Important cost factors include the number of state copies and measurement settings, as well as classical postprocessing time and memory. In this work, we present and analyze an online tomography algorithm that is designed to optimize all the aforementioned resources at the cost of a worse dependence on accuracy. The protocol is the first to give optimal performance in terms of rank and dimension for state copies, measurement settings and memory. Classical runtime is also reduced substantially. Further improvements are possible by executing the algorithm on a quantum computer, giving a quantum speedup for quantum state tomography.

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来自少数基础测量的快速而稳健的量子态断层扫描

量子态断层扫描是用于众多量子信息处理任务的强大但资源密集型的通用解决方案。这促使设计稳健的断层扫描程序，尽可能少地使用相关资源。重要的成本因素包括状态副本和测量设置的数量，以及经典的后处理时间和内存。在这项工作中，我们提出并分析了一种在线断层扫描算法，该算法旨在以对准确性的依赖性更差为代价来优化所有上述资源。该协议是第一个在状态副本、测量设置和内存的等级和维度方面提供最佳性能的协议。经典运行时间也大大减少。通过在量子计算机上执行算法，可以进一步改进，