Importance of Correlations for Neural Quantum States

Fuente: arXiv
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Main Authors: Döschl, Fabian, Bohrdt, Annabelle
Format: Preprint
Published: 2025
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author Döschl, Fabian
Bohrdt, Annabelle
author_facet Döschl, Fabian
Bohrdt, Annabelle
contents 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 for NQS-like quantum state representation by employing a correlation-based interpretable neural network architecture and thereafter proving our observations based on Boolean function theory. The correlator neural network demonstrates that, even for simple product states, up to all system-size correlation orders in the chosen computational basis are required to represent a quantum state faithfully. We explain these observations using the Fourier expansion, which reveals the correlator basis as the effective basis of the internal NQS structure, the resulting necessity for high-order correlations, potential linear dependencies in constrained Hilbert spaces, and connections between spin basis-rotations and the correlator basis. Furthermore, we analyze how activation functions, network architectures, and choice of reference basis influence correlation requirements. Our results provide new insights and a better understanding of the internal structure and requirements of NQS, enabling a more systematic use of NQS in future research.
format Preprint
id arxiv_https___arxiv_org_abs_2508_14152
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Importance of Correlations for Neural Quantum States
Döschl, Fabian
Bohrdt, Annabelle
Quantum Physics
Disordered Systems and Neural Networks
Quantum Gases
Strongly Correlated Electrons
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 for NQS-like quantum state representation by employing a correlation-based interpretable neural network architecture and thereafter proving our observations based on Boolean function theory. The correlator neural network demonstrates that, even for simple product states, up to all system-size correlation orders in the chosen computational basis are required to represent a quantum state faithfully. We explain these observations using the Fourier expansion, which reveals the correlator basis as the effective basis of the internal NQS structure, the resulting necessity for high-order correlations, potential linear dependencies in constrained Hilbert spaces, and connections between spin basis-rotations and the correlator basis. Furthermore, we analyze how activation functions, network architectures, and choice of reference basis influence correlation requirements. Our results provide new insights and a better understanding of the internal structure and requirements of NQS, enabling a more systematic use of NQS in future research.
title Importance of Correlations for Neural Quantum States
topic Quantum Physics
Disordered Systems and Neural Networks
Quantum Gases
Strongly Correlated Electrons
url https://arxiv.org/abs/2508.14152