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Article Abstract
We present a least square state estimator regularized by state purity to accomplish the task of quantum state tomography and entanglement verification, and report an experimental validation on a superconducting processor. First, a scalable full-state tomography is achieved with state fidelity 0.8217(1) for the 9-qubit W state and 0.6817(1) for the 17-qubit Greenberger-Horne-Zeilinger state, with the latter reaching 0.7587(1) under a pure-state assumption. Then, the presence of genuine multiqubit entanglement in the majority of generated states is conclusively certified by violating the corresponding entanglement witness. Finally, it is demonstrated that our method can achieve superior tomography accuracy with limited measurement settings and that mitigating error is essential for leveraging noisy quantum systems in quantum processing tasks. Our results pave the way for more accurate full characterization of larger-scale many-body quantum systems.
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