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  • Open Access

Neural quantum states for entanglement-depth certification from randomized Pauli measurements

Marcin Płodzień*

  • *Contact author: marcin.plodzien@qilimanjaro.tech
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Phys. Rev. Research 8, 023255 – Published 8 June, 2026

DOI: https://doi.org/10.1103/29hj-7w41

Abstract

Entanglement depth quantifies how many qubits share genuine multipartite entanglement, but certification typically relies on tailored witnesses or full tomography, both of which scale poorly with system size. We recast entanglement-depth and non-k-separability certification as likelihood-based model selection among neural quantum states whose architecture enforces a chosen entanglement constraint. A hierarchy of separable neural quantum states is trained on finite-shot local Pauli outcomes and compared against an unconstrained reference model trained on the same data. When all constrained models are statistically disfavored, the data certify entanglement beyond the imposed limit directly from measurement statistics, without reconstructing the density matrix. We validate the method on simulated six- and ten-qubit datasets targeting Greenberger–Horne–Zeilinger state (GHZ), Dicke, and Bell-pair states, and demonstrate robustness for mixed states under local noise. Finally, we discuss lightweight interpretability diagnostics derived from trained parameters that expose coarse entanglement patterns and qubit groupings directly from bitstring statistics.

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Phys. Rev. Research 8, 023255– Published 8 June, 2026
  • Received 22 December 2025
  • Accepted 21 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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