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    Prescriptive preparation and verification of nonstabilizer states

    Jian Li1, Ye-Chao Liu2,1,*, Xiao-Xiao Chen1, Zhe Meng1, Xing-Yan Fan1, Wen-Hao Wang1, Jie Ma1, An-Ning Zhang1,†, and Jiangwei Shang1,‡

    • *Contact author: liu@zib.de
    • †Contact author: anningzhang@bit.edu.cn
    • ‡Contact author: jiangwei.shang@bit.edu.cn

    Phys. Rev. Applied 26, 014074 – Published 23 July, 2026

    DOI: https://doi.org/10.1103/4hxp-fswy

    Abstract

    High-fidelity quantum-state preparation is a central task in quantum information science. In practice, it is commonly guided either by full quantum state tomography, which becomes prohibitively resource-intensive as system size grows, or by empirically chosen measurement settings that lack principled optimality. Here, we show that quantum state verification (QSV) can be elevated from a purely diagnostic tool to a prescriptive framework for quantum-state preparation, directly specifying experimentally optimal measurements and quantitative fidelity indicators without full state reconstruction. We experimentally realize this prescriptive paradigm using a three-qubit nonstabilizer W state and a modified homogeneous QSV protocol. The verification measurements not only certify the prepared state with high confidence but also serve as a tomography-free indicator that systematically informs the preparation procedure. Using only nine measurement settings and 104 samples, we achieve high-fidelity state preparation consistent with full tomography that requires orders of magnitude more resources. Beyond the present implementation, the prescriptive structure of QSV is naturally compatible with closed-loop feedback control, outlining a pathway toward genuine real-time quantum-state preparation in future low-latency platforms.

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