Importance of Correlations for Neural Quantum States

• URL: http://arxiv.org/abs/2508.14152v1
• Date: Tue, 19 Aug 2025 17:55:21 GMT
• Title: Importance of Correlations for Neural Quantum States
• Abstract summary: Neural quantum states (NQS) have emerged as a powerful variational ansatz for representing quantum many-body wave functions.<n>We investigate the role of correlations for NQS-like quantum state representation by employing a correlation-based interpretable neural network architecture.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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