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Solving the quantum many-body problem with artificial neural networks
Open accessAbstract
Machine learning and quantum physics: Elucidating the behavior of quantum interacting systems of many particles remains one of the biggest challenges in physics. Traditional numerical methods often work well, but some of the most interesting problems leave them stumped. Carleo and Troyer harnessed the power of machine learning to develop a variational approach to the quantum many-body problem (see the Perspective by Hush). The method performed at least as well as state-of-the-art approaches, setting a benchmark for a prototypical two-dimensional problem. With further development, it may well prove a valuable piece in the quantum toolbox. Science , this issue p. 602 ; see also p. 580
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“In practice, the matrix S is typically ill-conditioned and needs to be regularized, for which there exist several approaches 47,56,121 .”
From Beyond-classical computation in quantum simulation (2025) · cites this paper as [47]
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Cites
LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
Equation of State Calculations by Fast Computing Machines
Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953) · The Journal of Chemical Physics · doi:10.1063/1.1699114 · Cited by 37,192
Reducing the dimensionality of data with neural networks
Hinton, G. E., & Salakhutdinov, R. R. (2006) · Science · doi:10.1126/science.1127647 · Cited by 20,928
Messiah, A. (1961) · Cited by 16,012
Mastering the game of Go with deep neural networks and tree search
Silver, D., Huang, A., Maddison, C. J., Guez, A., Sifre, L., van den Driessche, G., Schrittwieser, J., Antonoglou, I., Panneershelvam, V., Lanctot, M., et al. (2016) · Nature · doi:10.1038/nature16961 · Cited by 15,612
Density matrix formulation for quantum renormalization groups
White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
Approximation capabilities of multilayer feedforward networks
Hornik, K. (1991) · Neural Networks · doi:10.1016/0893-6080(91)90009-t · Cited by 6,091
The density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
Note on Exchange Phenomena in the Thomas Atom
Dirac, P. A. M. (1930) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100016108 · Cited by 3,302
Colloquium: Nonequilibrium dynamics of closed interacting quantum systems
Polkovnikov, A., Sengupta, K., Silva, A., & Vengalattore, M. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.863 · Cited by 2,562
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- J.Carrasquilla R. G.Melko https://arxiv.org/abs/1605.01735 (2016). · arXiv
- M. H.Amin E.Andriyash J.Rolfe B.Kulchytskyy R.Melko https://arxiv.org/abs/1601.02036 (2016). · arXiv
- Y. I. Frenkel Wave Mechanics: Advanced General Theory (International Series of Monographs on Nuclear Energy: Reactor Design Physics The Clarendon Press 1934).
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Biamonte, J., Wittek, P., Pancotti, N., Rebentrost, P., Wiebe, N., & Lloyd, S. (2017) · Nature · doi:10.1038/nature23474 · Cited by 4,779
Recent advances and applications of machine learning in solid-state materials science
Schmidt, J., Marques, M. R. G., Botti, S., & Marques, M. A. L. (2019) · npj Computational Materials · doi:10.1038/s41524-019-0221-0 · Cited by 2,736
Machine learning and the physical sciences
Carleo, G., Cirac, J. I., Cranmer, K. S., Daudet, L., Schuld, M., Tishby, N., Vogt-Maranto, L., & Zdeborová, L. (2019) · Reviews of Modern Physics · doi:10.1103/revmodphys.91.045002 · Cited by 2,640
Self-citationScientific discovery in the age of artificial intelligence.
Wang, H., Fu, T., Du, Y., Gao, W., Huang, K., Liu, Z., Chandak, P., Liu, S., Van Katwyk, P., Deac, A., et al. (2023) · Nature · doi:10.1038/s41586-023-06221-2 · Cited by 1,823
Noisy intermediate-scale quantum algorithms
Bharti, K., Cervera-Lierta, A., Kyaw, T. H., Haug, T., Alperin-Lea, S., Anand, A., Degroote, M., Heimonen, H., Kottmann, J. S., Menke, T., et al. (2022) · Reviews of Modern Physics · doi:10.1103/revmodphys.94.015004 · Cited by 2,231
Metadata
- Authors
- Carleo, G., & Troyer, M.
- Affiliations
- ETH Zurich (CH)
- Microsoft (United States) (US)
- Corresponding author
- Carleo, Giuseppe
- Venue
- Science
- Published
- 2017-02-10
- Volume
- 355
- Issue
- 6325
- Pages
- 602-606
- ISSN
- 0036-8075 (ISSN-L)
- 1095-9203
- OpenAlex
- W2419175238
- Cited by
- 2,215
- References
- 53
- Citations by year
- 2026: 178 · 2025: 297 · 2024: 257 · 2023: 250 · 2022: 289 · 2021: 303 · 2020: 255 · 2019: 208 · 2018: 132 · 2017: 46
- FWCI
- 86.50
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Science (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Funders
- European Commission Directorate-General for Research and Innovation (award287220)
- Microsoft Research (award287221)
- Lincoln Laboratory (award287222)
- Swiss National Science Foundation (award287223)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Cold Atom Physics and Bose-Einstein Condensates
- Keywords
- quantum many-body problem, artificial neural networks, variational quantum states, reinforcement learning, ground state, unitary evolution
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