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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.23468 |
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| _version_ | 1866918407093354496 |
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| author | Lu, Yiming Bharadwaj, Sriram Rathore, Dikshant Luo, Di |
| author_facet | Lu, Yiming Bharadwaj, Sriram Rathore, Dikshant Luo, Di |
| contents | We establish an information-theoretic scaling law for generic autoregressive neural quantum states, determined by the middle-cut mutual information of the wavefunction amplitude. By formalizing the virtual bond as an effective information channel across a sequence bipartition, we rigorously prove that exact autoregressive representation of a quantum state requires the virtual-bond dimension to scale with the amplitude mutual information. For stabilizer-state families, we show that this law yields an explicit, analytical rank formula. Applying this framework across quantum-state tomography, ground-state and finite-temperature learning, our numerical experiments expose precise exponent matching, architecture-dependent scaling differences between recurrent and Transformer neural quantum state, and the critical role of autoregressive basis ordering. These results establish a rigorous physical link between the intrinsic structure of a quantum many-body state and the corresponding neural-network capacity required for its faithful representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23468 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Information-Theoretic Scaling Laws of Neural Quantum States Lu, Yiming Bharadwaj, Sriram Rathore, Dikshant Luo, Di Quantum Physics We establish an information-theoretic scaling law for generic autoregressive neural quantum states, determined by the middle-cut mutual information of the wavefunction amplitude. By formalizing the virtual bond as an effective information channel across a sequence bipartition, we rigorously prove that exact autoregressive representation of a quantum state requires the virtual-bond dimension to scale with the amplitude mutual information. For stabilizer-state families, we show that this law yields an explicit, analytical rank formula. Applying this framework across quantum-state tomography, ground-state and finite-temperature learning, our numerical experiments expose precise exponent matching, architecture-dependent scaling differences between recurrent and Transformer neural quantum state, and the critical role of autoregressive basis ordering. These results establish a rigorous physical link between the intrinsic structure of a quantum many-body state and the corresponding neural-network capacity required for its faithful representation. |
| title | Information-Theoretic Scaling Laws of Neural Quantum States |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2603.23468 |