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  • Open Access

Towards interpretability of neural quantum states

Fabian Döschl* and Annabelle Bohrdt

  • *Contact author: Fa.Doeschl@physik.uni-muenchen.de
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Phys. Rev. B 114, 245114 – Published 13 October, 2026

DOI: https://doi.org/10.1103/2cfz-dm5f

Abstract

Neural quantum states (NQS) have emerged as a powerful variational ansatz for representing quantum many-body wave functions. Their internal mechanisms, however, remain poorly understood. We investigate the role of correlations in NQS-like quantum state representation by employing a correlation-based interpretable neural network architecture and then proving our observations using Boolean function theory. The correlator neural network demonstrates that, even for simple product states, correlations up to the systemsize in the chosen computational basis are required to represent a quantum state faithfully. We explain these observations using Fourier expansion, which reveals the correlator basis as the effective basis of the internal NQS structure, the resulting necessity for high-order correlations as supported by an entanglement bound that scales with the correlation order, the consequences of linear dependencies in constrained Hilbert spaces for correlation requirements, and the connections between spin basis rotations and the correlator basis. Furthermore, we analyze how neural networks achieve high correlation orders by increasing the magnitude of the network weights, which can be compensated by increasing the network depth. Lastly, we discuss how activation functions, network architectures, and the choice of reference basis influence correlation requirements. Our results provide insights and a better understanding of the internal structure and requirements of NQS, enabling a more systematic use of NQS in future research.

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Phys. Rev. B 114, 245114– Published 13 October, 2026
  • Received 24 October 2025
  • Revised 15 June 2026
  • Accepted 13 August 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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