The DOI matches its Crossref record; 25 of the 25 references it cites were found in a registry or an index.
Efficient representation of quantum many-body states with deep neural networks
Open accessAbstract
Part of the challenge for quantum many-body problems comes from the difficulty of representing large-scale quantum states, which in general requires an exponentially large number of parameters. Neural networks provide a powerful tool to represent quantum many-body states. An important open question is what characterizes the representational power of deep and shallow neural networks, which is of fundamental interest due to the popularity of deep learning methods. Here, we give a proof that, assuming a widely believed computational complexity conjecture, a deep neural network can efficiently represent most physical states, including the ground states of many-body Hamiltonians and states generated by quantum dynamics, while a shallow network representation with a restricted Boltzmann machine cannot efficiently represent some of those states.
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Cites
LeCun, Y., Bengio, Y., & Hinton, G. (2015) · Nature · doi:10.1038/nature14539 · Cited by 84,126
Fault-tolerant quantum computation by anyons
Kitaev, A. Y. (2003) · Annals of Physics · doi:10.1016/s0003-4916(02)00018-0 · Cited by 7,238
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
Raussendorf, R., & Briegel, H. J. (2001) · Physical Review Letters · doi:10.1103/physrevlett.86.5188 · Cited by 4,477
Elementary gates for quantum computation
Barenco, A., Bennett, C. H., Cleve, R., DiVincenzo, D. P., Margolus, N., Shor, P., Sleator, T., Smolin, J. A., & Weinfurter, H. (1995) · Physical Review A · doi:10.1103/physreva.52.3457 · Cited by 4,311
Lloyd, S. (1996) · Science · doi:10.1126/science.273.5278.1073 · Cited by 3,088 · cited 1×
“Most physically relevant quantum states are either generated by many-body dynamics, which can be efficiently simulated through a polynomial size quantum circuit [11–13] , or as ground states of some k -local Hamiltonians.”
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
Efficient Simulation of One-Dimensional Quantum Many-Body Systems
Vidal, G. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.040502 · Cited by 1,779
Verstraete, F., Murg, V., & Cirac, J. I. (2008) · Advances in Physics · doi:10.1080/14789940801912366 · Cited by 1,762
Computational Complexity: A Modern Approach
Arora, S., & Barak, B. (2009) · doi:10.1017/cbo9780511804090 · Cited by 1,690
Cited by
Expressive power of parametrized quantum circuits
Du, Y., Hsieh, M.-H., Liu, T., & Tao, D. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033125 · Cited by 318
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
Machine learning meets quantum foundations: A brief survey
Bharti, K., Haug, T., Vedral, V., & Kwek, L.-C. (2020) · AVS Quantum Science · doi:10.1116/5.0007529 · Cited by 59
Metadata
- Authors
- Gao, X., & Duan, L.-M.
- Venue
- Nature Communications
- Published
- 2017-09-22
- Volume
- 8
- Issue
- 1
- Pages
- 662-662
- ISSN
- 2041-1723 (ISSN-L)
- OpenAlex
- W2580506952
- Cited by
- 346
- References
- 25
- FWCI
- 19.69
- Type
- journal article
- Language
- en
- Open access
- gold
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
