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Approximating quantum many-body wave functions using artificial neural networks
Open accessAbstract
In this paper, we demonstrate the expressibility of artificial neural networks (ANNs) in quantum many-body physics by showing that a feed-forward neural network with a small number of hidden layers can be trained to approximate with high precision the ground states of some notable quantum many-body systems. We consider the one-dimensional free bosons and fermions, spinless fermions on a square lattice away from half-filling, as well as frustrated quantum magnetism with a rapidly oscillating ground-state characteristic function. In the latter case, an ANN with a standard architecture fails, while that with a slightly modified one successfully learns the frustration-induced complex sign rule in the ground state and approximates the ground states with high precisions. As an example of practical use of our method, we also perform the variational method to explore the ground state of an antiferromagnetic ${J}_{1}\text{\ensuremath{-}}{J}_{2}$ Heisenberg model.
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Multilayer feedforward networks are universal approximators
Hornik, K., Stinchcombe, M., & White, H. (1989) · Neural Networks · doi:10.1016/0893-6080(89)90020-8 · Cited by 21,728
Approximation by superpositions of a sigmoidal function
Cybenko, G. (1989) · Mathematics of Control, Signals, and Systems · doi:10.1007/bf02551274 · Cited by 13,883
Density matrix formulation for quantum renormalization groups
White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
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
Solving the quantum many-body problem with artificial neural networks
Carleo, G., & Troyer, M. (2017) · Science · doi:10.1126/science.aag2302 · Cited by 2,215
Machine learning phases of matter
Carrasquilla, J., & Melko, R. G. (2017) · Nature Physics · doi:10.1038/nphys4035 · Cited by 1,448
Why Does Deep and Cheap Learning Work So Well?
Lin, H. W., Tegmark, M., & Rolnick, D. (2017) · Journal of Statistical Physics · doi:10.1007/s10955-017-1836-5 · Cited by 393
Cited by
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Iten, R., Metger, T., Wilming, H., del Rio, L., & Renner, R. (2020) · Physical Review Letters · doi:10.1103/physrevlett.124.010508 · Cited by 458
Beck, C., E, W., & Jentzen, A. (2019) · Journal of Nonlinear Science · doi:10.1007/s00332-018-9525-3 · Cited by 308
Quantum Entanglement in Deep Learning Architectures
Levine, Y., Sharir, O., Cohen, N., & Shashua, A. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.065301 · Cited by 206
Information Perspective to Probabilistic Modeling: Boltzmann Machines versus Born Machines
Cheng, S., Chen, J., & Wang, L. (2018) · Entropy · doi:10.3390/e20080583 · Cited by 104
Quenches near Ising quantum criticality as a challenge for artificial neural networks
Czischek, S., Gärttner, M., & Gasenzer, T. (2018) · Physical Review B · doi:10.1103/physrevb.98.024311 · Cited by 85
Metadata
- Authors
- Cai, Z., & Liu, J.
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2018-01-09
- Volume
- 97
- Issue
- 3
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2610038766
- Cited by
- 214
- References
- 7
- FWCI
- 12.97
- Type
- journal article
- Language
- en
- Open access
- green
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