Optimal and robust quantum state tomography of star-topology register

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.