Importance of Correlations for Neural Quantum States
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916909287473152 |
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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 |
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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 |