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  • Open Access

Learning minimal representations of fermionic ground states

Felix Frohnert*, Emiel Koridon, and Stefano Polla†

  • *Contact author: f.frohnert@liacs.leidenuniv.nl
  • †Contact author: polla@lorentz.leidenuniv.nl
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Phys. Rev. Research 8, 033014 – Published 6 July, 2026

DOI: https://doi.org/10.1103/qsl5-cyq2

Abstract

We introduce an unsupervised machine-learning framework that discovers optimally compressed representations of quantum many-body ground states. Using an autoencoder neural network architecture on reduced density matrix data from L-site Fermi-Hubbard models, we identify minimal latent spaces with a sharp reconstruction quality threshold at L−1 latent dimensions, matching the system's intrinsic degrees of freedom. We demonstrate the use of the trained decoder as a differentiable variational ansatz to minimize energy directly within the latent space. Crucially, this approach circumvents the N-representability problem, as the learned manifold implicitly restricts the optimization to physically valid quantities.

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Phys. Rev. Research 8, 033014– Published 6 July, 2026
  • Received 4 February 2026
  • Accepted 27 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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