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Entanglement and optimization within autoregressive neural quantum states

Andrew Jreissaty1,2,*, Hang Zhang1, Jairo C. Quijano3, Juan Carrasquilla1,2, and Roeland Wiersema4

  • *Contact author: ajreissaty@phys.ethz.ch
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Phys. Rev. Research 8, 013147 – Published 10 February, 2026

DOI: https://doi.org/10.1103/t2cg-kr7y

Abstract

Neural quantum states (NQSs) are powerful variational ansätze capable of representing highly entangled quantum many-body wavefunctions. While the average entanglement properties of ensembles of restricted Boltzmann machines are well understood, the entanglement structure of autoregressive NQSs such as recurrent neural networks and transformers remains largely unexplored. We perform large-scale simulations of ensembles of random autoregressive wavefunctions for chains of up to 256 spins and uncover signatures of transitions in their average entanglement scaling, entanglement spectra, and correlation functions. We show that the standard softmax normalization of the wavefunction suppresses entanglement and fluctuations, and introduce a square modulus normalization function that restores them. Finally, we connect the insights gained from our entanglement and activation function analysis to initialization strategies for finding the ground states of strongly correlated Hamiltonians via variational Monte Carlo.

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Phys. Rev. Research 8, 013147– Published 10 February, 2026
  • Received 22 September 2025
  • Accepted 12 January 2026
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