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$\widetilde{O}(N^2)$ Representation of General Continuous Anti-symmetric Function

Published 23 Feb 2024 in quant-ph | (2402.15167v2)

Abstract: In quantum mechanics, the wave function of fermion systems such as many-body electron systems are anti-symmetric (AS) and continuous, and it is crucial yet challenging to find an ansatz to represent them. This paper addresses this challenge by presenting an ${\widetilde O}(N2)$ ansatz based on permutation-equivariant functions. We prove that our ansatz can represent any AS continuous functions, and can accommodate the determinant-based structure proposed by Hutter [14], solving the proposed open problems that ${O}(N)$ Slater determinants are sufficient to provide universal representation of AS continuous functions. Together, we offer a generalizable and efficient approach to representing AS continuous functions, shedding light on designing neural networks to learn wave functions.

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References (30)
  1. James B Anderson. A random-walk simulation of the schrödinger equation: H+ 3. The Journal of Chemical Physics, 63(4):1499–1503, 1975.
  2. Nonrelativistic energy levels of helium atoms. Physical Review A, 98(1):012510, 2018.
  3. Solving the quantum many-body problem with artificial neural networks. Science, 355(6325):602–606, 2017.
  4. Exact and efficient representation of totally anti-symmetric functions. arXiv preprint arXiv:2311.05064, 2023.
  5. Fermionic neural-network states for ab-initio electronic structure. Nature communications, 11(1):2368, 2020.
  6. The feynman lectures on physics; vol. 3. American Journal of Physics, 33(9):750–752, 1965.
  7. Quantum monte carlo simulations of solids. Reviews of Modern Physics, 73(1):33, 2001.
  8. Nuclei with up to a= 6 nucleons with artificial neural network wave functions. Few-Body Systems, 63(1):7, 2022.
  9. Solving high-dimensional partial differential equations using deep learning. Proceedings of the National Academy of Sciences, 115(34):8505–8510, 2018.
  10. Alexander Heifetz. Quantum mechanics in drug discovery. Springer, 2020.
  11. Deep-neural-network solution of the electronic schrödinger equation. Nature Chemistry, 12(10):891–897, 2020.
  12. Recurrent neural network wave functions. Physical Review Research, 2(2):023358, 2020.
  13. Geometry of backflow transformation ansatze for quantum many-body fermionic wavefunctions. Communications in Mathematical Sciences, 21(5):1447–1453, 2023.
  14. Marcus Hutter. On representing (anti) symmetric functions. arXiv preprint arXiv:2007.15298, 2020.
  15. Geometry dependence of the sign problem in quantum monte carlo simulations. Phys. Rev. B, 92:045110, Jul 2015. doi: 10.1103/PhysRevB.92.045110. URL https://link.aps.org/doi/10.1103/PhysRevB.92.045110.
  16. B Keimer and JE Moore. The physics of quantum materials. Nature Physics, 13(11):1045–1055, 2017.
  17. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25, 2012.
  18. Hermann G Kümmel. A biography of the coupled cluster method. International Journal of Modern Physics B, 17(28):5311–5325, 2003.
  19. Fast parallel algorithms for vandermonde determinants. International Journal of Computer Mathematics, 73(4):479–486, 2000. doi: 10.1080/00207160008804911. URL https://doi.org/10.1080/00207160008804911.
  20. Forward laplacian: A new computational framework for neural network-based variational monte carlo. arXiv preprint arXiv:2307.08214, 2023.
  21. Variational and diffusion quantum monte carlo calculations with the casino code. The Journal of chemical physics, 152(15):154106, 2020.
  22. Sign problem in quantum monte carlo simulation. arXiv preprint arXiv:2204.08777, 2022.
  23. o⁢(n2)𝑜superscript𝑛2o(n^{2})italic_o ( italic_n start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ) universal antisymmetry in fermionic neural networks. arXiv preprint arXiv:2205.13205, 2022.
  24. Neural-network quantum states for periodic systems in continuous space. Physical Review Research, 4(2):023138, 2022.
  25. Ab initio solution of the many-electron schrödinger equation with deep neural networks. Physical Review Research, 2(3):033429, 2020.
  26. Arthur Sard. The measure of the critical values of differentiable maps. 1942.
  27. Victor A Toponogov. Differential geometry of curves and surfaces. Springer, 2006.
  28. Attention is all you need. Advances in neural information processing systems, 30, 2017.
  29. A self-attention ansatz for ab-initio quantum chemistry. arXiv preprint arXiv:2211.13672, 2022.
  30. Towards antisymmetric neural ansatz separation. arXiv preprint arXiv:2208.03264, 2022.

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