While quantum state tomography plays a vital role in the verification and benchmarking of quantum systems, it is an intractable task if the controllability of the quantum registers is constrained. In this paper, we propose a novel scheme for optimal and robust quantum state tomography for systems with constrained controllability. Based on the specific symmetry, we decompose the Hilbert space to alleviate the complexity of tomography and design a compact strategy with the minimum number of measurements. To switch between these measurement settings, we adopted parameterized quantum circuits consisting of local operations and free evolution, which are easy to implement in most practical systems. Then the parameters of these circuits were optimized to improve the robustness against errors of measurements. We demonstrated the experimental feasibility of our method on a 4-spin star-topology register and numerically studied its ability to characterize large-scale systems on a 10-spin star-topology register, respectively. Our results can help future investigations of quantum systems with constrained ability of quantum control and measurement.

中文翻译：

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星形拓扑寄存器的最佳且鲁棒的量子态层析成像


虽然量子态断层扫描在量子系统的验证和基准测试中发挥着至关重要的作用，但如果量子寄存器的可控性受到限制，这将是一项棘手的任务。在本文中，我们提出了一种针对可控性受限的系统的最佳且鲁棒的量子态层析成像的新方案。基于特定的对称性，我们分解希尔伯特空间以减轻层析成像的复杂性，并设计具有最少测量次数的紧凑策略。为了在这些测量设置之间切换，我们采用了由局部操作和自由演化组成的参数化量子电路，这在大多数实际系统中都很容易实现。然后对这些电路的参数进行优化，以提高针对测量误差的鲁棒性。我们证明了我们的方法在 4 自旋星形拓扑寄存器上的实验可行性，并分别在数值上研究了其在 10 自旋星形拓扑寄存器上表征大规模系统的能力。我们的结果可以帮助未来对量子控制和测量能力有限的量子系统的研究。