Cited by 274Quantum many-body systemsQuantum Computing Algorithms and ArchitectureAdvanced Chemical Physics Studies

Recurrent neural network wave functions

Open access
Hibat-Allah, Mohamed, Ganahl, Martin, Hayward, Lauren E., Melko, Roger G., Carrasquilla, Juan·2020·Physical Review Research

Abstract

This paper introduces a new class of computationally tractable wavefunctions, called recurrent neural network wavefunctions, based on recurrent neural network technology. The authors show that these wavefunctions outperform optimization methods for strongly correlated many-body systems with less variational parameters.

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.1103/physrevresearch.2.023358

Cites

8 of 8 references verified0 citation errors · 0 not checkable

Statistics

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

  • In order to efficiently estimate the infidelity, the authors of Ref. 138 propose a control-variate method to reduce the variance of the estimator similar to Ref. 123.

    “In order to efficiently estimate the infidelity, the authors of Ref. 138 propose a control-variate method to reduce the variance of the estimator similar to Ref. 123.”

    From Beyond-classical computation in quantum simulation (2025) · cites this paper as [123]

    Appendix C proposes a variance-reduction term for estimating energy gradients and says it is similar in spirit to control-variate methods. It does not propose the method for estimating infidelity; the estimator described there is for gradients in variational Monte Carlo. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Cites

Flagged first, then by citations

Research works printed but not linked: 78

  1. A. Krizhevsky, I. Sutskever, and G. E. Hinton, Imagenet classification with deep convolutional neural networks, in Proceedings of the 25th International Conference on Neu- ral Information Processing Systems, Neural Information Pro- cessing Systems Vol. 12 (Curran, New York, 2012), Vol. 1, pp. 1097-1105.
  2. Y. LeCun, Y. Bengio, and G. Hinton, Deep learning, Nature (London) 521, 436 (2015). · DOI · Paper page
  3. K. He, X. Zhang, S. Ren, and J. Sun, Deep residual learning for image recognition, in Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition (IEEE, 2016), pp. 770-778.
  4. J. Vamathevan, D. Clark, P. Czodrowski, I. Dunham, E. Ferran, G. Lee, B. Li, A. Madabhushi, P. Shah, M. Spitzer, and S. Zhao, Applications of machine learning in drug discovery and development, Nat. Rev. Drug Discov. 18, 463 (2019). · DOI · Paper page
  5. C. Badue, R. Guidolini, R. V. Carneiro, P. Azevedo, V. B. Cardoso, A. Forechi, L. Jesus, R. Berriel, T. Paixão, F. Mutz, L. Veronese, T. Oliveira-Santos, and A. F. De Souza, Self-driving cars: A survey, arXiv:1901.04407 (2019). · arXiv
  6. D. Silver, J. Schrittwieser, K. Simonyan, I. Antonoglou, A. Huang, A. Guez, T. Hubert, L. Baker, M. Lai, A. Bolton, Y. Chen, T. Lillicrap, F. Hui, L. Sifre, G. van den Driessche, T. Graepel, and D. Hassabis, Mastering the game of go without human knowledge, Nature (London) 550, 354 (2017). · DOI · Paper page
  7. G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborová, Machine learn- ing and the physical sciences, Rev. Mod. Phys. 91, 045002 (2019). · DOI
  8. P. Hohenberg and W. Kohn, Inhomogeneous electron gas, Phys. Rev. 136, B864 (1964). · DOI · Paper page
  9. J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of superconductivity, Phys. Rev. 108, 1175 (1957). · DOI
  10. F. Becca and S. Sorella, Quantum Monte Carlo Approaches for Correlated Systems (Cambridge University, Cambridge, England, 2017).
  11. R. Orús, Tensor networks for complex quantum systems, Nat. Rev. Phys. 1, 538 (2019). · DOI
  12. J. Androsiuk, L. Kulak, and K. Sienicki, Neural network so- lution of the Schrödinger equation for a two-dimensional har- monic oscillator, Chem. Phys. 173, 377 (1993). · DOI
  13. I. E. Lagaris, A. Likas, and D. I. Fotiadis, Artificial neural net- work methods in quantum mechanics, Comput. Phys. Commun. 104, 1 (1997). · DOI
  14. M. Sugawara, Numerical solution of the Schrödinger equa- tion by neural network and genetic algorithm, Comput. Phys. Commun. 140, 366 (2001). · DOI
  15. R. G. Melko, G. Carleo, J. Carrasquilla, and J. I. Cirac, Re- stricted Boltzmann machines in quantum physics, Nat. Phys. 15, 887 (2019). · DOI
  16. S. Hochreiter and J. Schmidhuber, Long short-term memory, Neural Comput. 9, 1735 (1997). · DOI · Paper page
  17. A. Graves, Supervised sequence labelling, in Supervised Se- quence Labelling with Recurrent Neural Networks (Springer, New York, 2012), pp. 5-13.
  18. K. Cho, B. van Merrienboer, C. Gulcehre, D. Bahdanau, F. Bougares, H. Schwenk, and Y. Bengio, Learning Phrase Rep- resentations using RNN Encoder-Decoder for Statistical Ma- chine Translation, in Proceedings of the 2014 Conference on Empirical Methods in Natural Language Processing (EMNLP) (Association for Computational Linguistics, Doha, Qatar, 2014), pp. 1724-1734.
  19. J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, Empirical evalu- ation of gated recurrent neural networks on sequence modeling, arXiv:1412.3555 (2014). · arXiv
  20. Z. C. Lipton, J. Berkowitz, and C. Elkan, A critical re- view of recurrent neural networks for sequence learning, arXiv:1506.00019 (2015). · arXiv
  21. A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, L. Kaiser, and I. Polosukhin, Attention is all you Need, in Advances in Neural Information Processing Systems 30, edited by I.
  22. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran Associates, Inc., 2017), pp. 5998-6008.
  23. Z. Yang, Z. Dai, Y. Yang, J. Carbonell, R. Salakhutdinov, and Q. V. Le, Xlnet: Generalized Autoregressive Pretraining for Language Understanding, Advances in Neural Information Processing Systems 32, edited by H. Wallach, H. Larochelle, A. Beygelzimer, F. d'Alché-Buc, E. Fox, and R. Garnett (Curran Associates, Inc., 2019), pp. 5753-5763.
  24. J. Carrasquilla, G. Torlai, R. G. Melko, and L. Aolita, Recon- structing quantum states with generative models, Nat. Mach. Intell. 1, 155 (2019). · DOI
  25. B. Uria, M.-A. Côté, K. Gregor, I. Murray, and H. Larochelle, Neural autoregressive distribution estimation, J. Mach. Learn. Res. 17, 7184 (2016).
  26. D. Wu, L. Wang, and P. Zhang, Solving Statistical Mechanics Using Variational Autoregressive Networks, Phys. Rev. Lett. 122, 080602 (2019). · DOI
  27. I. Goodfellow, Y. Bengio, and A. Courville, Deep Learning (MIT, Cambridge, MA, 2016).
  28. I. Goodfellow, Nips 2016 tutorial: Generative adversarial net- works, arXiv:1701.00160 (2016). · arXiv
  29. Y. Bengio, P. Simard, and P. Frasconi, Learning long-term dependencies with gradient descent is difficult, IEEE Trans. Neural Netw. 5, 157 (1994). · DOI · Paper page
  30. J. F. Kolen and S. C. Kremer, Gradient flow in recurrent nets: The difficulty of learning longterm dependencies, in A Field Guide to Dynamical Recurrent Networks (IEEE, New York, 2001), pp. 237-243.
  31. R. Pascanu, T. Mikolov, and Y. Bengio, On the difficulty of training recurrent neural networks, in Proceedings of the International Conference on Machine Learning (ICML, 2013), pp. 1310-1318.
  32. M. Fannes, B. Nachtergaele, and R. F. Werner, Finitely corre- lated states on quantum spin chains, Commun. Math. Phys. 144, 443 (1992). · DOI · Paper page
  33. H. Shen, Mutual information scaling and expressive power of sequence models, arXiv:1905.04271 (2019). · arXiv
  34. K. Cho, B. van Merriënboer, D. Bahdanau, and Y. Bengio, On the properties of neural machine translation: Encoder-decoder approaches, in Proceedings of SSST-8, Eighth Workshop on Syntax, Semantics and Structure in Statistical Translation (As- sociation for Computational Linguistics, Doha, Qatar, 2014), pp. 103-111.
  35. S. Bravyi, D. P. Divincenzo, R. Oliveira, and B. M. Terhal, The complexity of stoquastic local Hamiltonian problems, Quantum Inf. Comput. 8, 361 (2008).
  36. G. Torlai, G. Mazzola, J. Carrasquilla, M. Troyer, R. Melko, and G. Carleo, Neural-network quantum state tomography, Nat. Phys. 14, 447 (2018). · DOI
  37. S. R. White, Density Matrix Formulation for Quantum Renor- malization Groups, Phys. Rev. Lett. 69, 2863 (1992). · DOI · Paper page
  38. C. Roberts, A. Milsted, M. Ganahl, A. Zalcman, B. Fontaine, Y. Zou, J. Hidary, G. Vidal, and S. Leichenauer, Tensornetwork: A library for physics and machine learning, arXiv:1905.01330 (2019). · arXiv
  39. S. T. Flammia, A. Hamma, T. L. Hughes, and X.-G. Wen, Topological Entanglement Rényi Entropy and Reduced Density Matrix Structure, Phys. Rev. Lett. 103, 261601 (2009). · DOI
  40. M. B. Hastings, I. González, A. B. Kallin, and R. G. Melko, Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations, Phys. Rev. Lett. 104, 157201 (2010). · DOI
  41. S. R. White and I. Affleck, Dimerization and incommensurate spiral spin correlations in the zigzag spin chain: Analogies to the Kondo lattice, Phys. Rev. B 54, 9862 (1996). · DOI
  42. S. Eggert, Numerical evidence for multiplicative logarith- mic corrections from marginal operators, Phys. Rev. B 54, R9612(R) (1996). · DOI
  43. F. Becca, L. Capriotti, A. Parola, and S. Sorella, Variational Wave Functions for Frustrated Magnetic Models, in Introduc- tion to Frustrated Magnetism: Materials, Experiments, Theory, edited by C. Lacroix, P. Mendels, and F. Mila (Springer, Berlin, Heidelberg, 2011), pp. 379-406.
  44. W Marshall, Antiferromagnetism, Proc. R. Soc. A 232, 48 (1955).
  45. K. Choo, T. Neupert, and G. Carleo, Two-dimensional frus- trated j 1 -j 2 model studied with neural network quantum states, Phys. Rev. B 100, 125124 (2019). · DOI
  46. G. Torlai, J. Carrasquilla, M. T. Fishman, R. G. Melko, and M. P. A. Fisher, Wavefunction positivization via automatic differentiation, arXiv:1906.04654 (2019). · arXiv
  47. J. Thibaut, T. Roscilde, and F. Mezzacapo, Long-range entangled-plaquette states for critical and frustrated quantum systems on a lattice, Phys. Rev. B 100, 155148 (2019). · DOI
  48. O. Sharir, Y. Levine, N. Wies, G. Carleo, and A. Shashua, Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems, Phys. Rev. Lett. 124, 020503 (2020). · DOI
  49. F. Verstraete and J. I. Cirac, Renormalization algorithms for quantum-many body systems in two and higher dimensions, arXiv:cond-mat/0407066 (2004). · arXiv
  50. S. Yan, David A. Huse, and S. R. White, Spin-liquid ground state of the s = 1/2 kagome heisenberg antiferromagnet, Science 332, 1173 (2011). · DOI
  51. G. Evenbly and G. Vidal, Tensor Network Renormalization, Phys. Rev. Lett. 115, 180405 (2015). · DOI
  52. Anders W. Sandvik, Computational studies of quantum spin systems, in Lectures on the Physics of Strongly Correlated Sys- tems XIV: Fourteenth Training Course in the Physics of Strongly Correlated Systems, edited by A. Avella and F. Mancini, AIP Conf. Proc. No. 1297 (AIP, New York, 2010).
  53. H. W. J. Blöte and Y. Deng, Cluster Monte Carlo simulation of the transverse Ising model, Phys. Rev. E 66, 066110 (2002). · DOI
  54. L. Vanderstraeten, J. Haegeman, P. Corboz, and F. Verstraete, Gradient methods for variational optimization of projected entangled-pair states, Phys. Rev. B 94, 155123 (2016). · DOI · Paper page
  55. A. van den Oord, N. Kalchbrenner, L. Espeholt, K. kavukcuoglu, O. Vinyals, and A. Graves, Conditional Image Generation with PixelCNN Decoders, in Advances in Neural Information Processing Systems 29, edited by D. D. Lee, M. Sugiyama, U. V. Luxburg, I. Guyon, and R. Garnett (Curran Associates, Inc., 2016), pp. 4790-4798.
  56. C. Gros, Criterion for a good variational wave function, Phys. Rev. B 42, 6835 (1990). · DOI
  57. R. Assaraf and M. Caffarel, Zero-variance zero-bias principle for observables in quantum monte carlo: Application to forces, J. Chem. Phys. 119, 10536 (2003). · DOI
  58. C. Hubig, J. Haegeman, and U. Schollwöck, Error estimates for extrapolations with matrix-product states, Phys. Rev. B 97, 045125 (2018). · DOI · Paper page
  59. M. C. Bañuls, D. A. Huse, and J. I. Cirac, Entanglement and its relation to energy variance for local one-dimensional Hamiltonians, Phys. Rev. B 101, 144305 (2020). · DOI
  60. M. Hermans and B. Schrauwen, Training and analysing deep recurrent neural networks, in Advances in Neural Information Processing Systems, edited by C. J. C. Burges, L. Bottou, M. Welling, Z. Ghahramani, and K. Q. Weinberger (Curran, New York, 2013), Vol. 26, pp. 190-198.
  61. S. Chang, Y. Zhang, W. Han, M. Yu, X. Guo, W. Tan, X. Cui, M. Witbrock, M. Hasegawa-Johnson, and T. S. Huang, Dilated recurrent neural networks, Advances in Neural Information Processing Systems 30, edited by I.
  62. Guyon, U. V. Luxburg, S. Bengio, H. Wallach, R. Fergus, S. Vishwanathan, and R. Garnett (Curran Associates, Inc., 2017), pp. 77-87.
  63. D. Bahdanau, K. Cho, and Y. Bengio, Neural machine transla- tion by jointly learning to align and translate, arXiv:1409.0473 (2014). · arXiv
  64. J. Martens, J. Ba, and M. Johnson, Kronecker-factored curva- ture approximations for recurrent neural networks, in Proceed- ings of the International Conference on Learning Representa- tions (ICLR, 2018).
  65. K. Choo, A. Mezzacapo, and G. Carleo, Fermionic neural- network states for ab-initio electronic structure, Nat. Commun. 11, 2368 (2020). · DOI
  66. J. Carrasquilla, D. Luo, F. Pérez, A. Milsted, B. K. Clark, M. Volkovs, and L. Aolita, Probabilistic simulation of quantum circuits with the transformer, arXiv:1912.11052 (2019). · arXiv
  67. C. Roth, Iterative retraining of quantum spin models using recurrent neural networks, arXiv:2003.06228 (2020). · arXiv
  68. J. Appleyard, T. Kocisky, and P. Blunsom, Optimiz- ing performance of recurrent neural networks on GPUs, arXiv:1604.01946 (2016). · arXiv
  69. A. van den Oord, N. Kalchbrenner, and K. Kavukcuoglu, Pixel Recurrent Neural Networks, in Proceedings of the 33rd Inter- national Conference on International Conference on Machine Learning, Vol. 48 (JMLR, New York, 2016), pp. 1747-1756.
  70. Y. Wu, S. Zhang, Y. Zhang, Y. Bengio, and R. R. Salakhutdinov, On multiplicative integration with recurrent neural networks, in Proceedings of the Advances in Neural Information Processing Systems (NeuIPS, 2016), pp. 2856-2864.
  71. A. W. Sandvik and G. Vidal, Variational Quantum Monte Carlo Simulations with Tensor-Network States, Phys. Rev. Lett. 99, 220602 (2007). · DOI
  72. S.-X. Zhang, Z.-Q. Wan, and H. Yao, Automatic differen- tiable Monte Carlo: Theory and application, arXiv:1911.09117 (2019). · arXiv
  73. D. P. Kingma and J. Ba, ADAM: A method for stochastic optimization, arXiv:1412.6980 (2014). · arXiv
  74. R. Assaraf and M. Caffarel, Zero-Variance Principle for Monte Carlo Algorithms, Phys. Rev. Lett. 83, 4682 (1999). · DOI
  75. S. Mohamed, M. Rosca, M. Figurnov, and A. Mnih, Monte Carlo gradient estimation in machine learning, arXiv:1906.10652 (2019). · arXiv
  76. R. S. Sutton, D. A. McAllester, S. P. Singh, and Y. Mansour, Policy gradient methods for reinforcement learn- ing with function approximation, in Proceedings of Advances in Neural Information Processing Systems (NeuIPS, 2000), pp. 1057-1063.
  77. E. Lieb and D. Mattis, Ordering energy levels of interacting spin systems, J. Math. Phys. 3, 749 (1962). · DOI · Paper page
  78. Z. Wang and E. J. Davis, Calculating Rényi entropies with neural autoregressive quantum states, in Proceedings of the Machine Learning and Physical Sciences Workshop (NeurIPS, 2019), arXiv:2003.01358. · arXiv

Cited by

Sorted by citations

Authors
Hibat-Allah, M., Ganahl, M., Hayward, L. E., Melko, R. G., & Carrasquilla, J.
Affiliations
  • University of Waterloo (CA)
  • Perimeter Institute (CA)
Venue
Physical Review Research
Published
2020-06-17
Volume
2
Issue
2
ISSN
2643-1564 (ISSN-L)
OpenAlex
W3005029016
Cited by
274
References
8
Citations by year
2026: 24 · 2025: 52 · 2024: 51 · 2023: 52 · 2022: 31 · 2021: 45 · 2020: 19
FWCI
15.05
Type
journal article
Language
en
Open access
Locations
  • Physical Review Research (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • arXiv (Cornell University)
Funders
  • Simons Foundation
  • Natural Sciences and Engineering Research Council of Canada
  • Canada Research Chairs
  • Canadian Institute for Advanced Research
  • National Science Foundation (NSF PHY-1748958)
  • Innovation, Science and Economic Development Canada
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 › Advanced Chemical Physics Studies
Keywords
variational quantum algorithms, strongly correlated systems, variational quantum eigensolver, variational parameters, quantum chemistry, quantum many-body simulation

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review