Impact Of Conditional Modelling For A Universal Autoregressive Quantum State

Massimo Bortone, Yannic Rath, and George H. Booth

Department of Physics, King’s College London, Strand, London WC2R 2LS, United Kingdom

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We present a generalized framework to adapt universal quantum state approximators, enabling them to satisfy rigorous normalization and autoregressive properties. We also introduce filters as analogues to convolutional layers in neural networks to incorporate translationally symmetrized correlations in arbitrary quantum states. By applying this framework to the Gaussian process state, we enforce autoregressive and/or filter properties, analyzing the impact of the resulting inductive biases on variational flexibility, symmetries, and conserved quantities. In doing so we bring together different autoregressive states under a unified framework for machine learning-inspired ansätze. Our results provide insights into how the autoregressive construction influences the ability of a variational model to describe correlations in spin and fermionic lattice models, as well as ab $initio$ electronic structure problems where the choice of representation affects accuracy. We conclude that, while enabling efficient and direct sampling, thus avoiding autocorrelation and loss of ergodicity issues in Metropolis sampling, the autoregressive construction materially constrains the expressivity of the model in many systems.

Popular summary

Computationally resolving interacting quantum particles, such as the electrons in a molecule, holds the promise to unlock many potential applications across a range of fields, from the design of new drugs to the discovery of exotic materials. However, this requires circumventing the exponential scaling of the quantum many-body wave function, the core mathematical object describing the behaviour of these electrons. Parameterizing these states with techniques inspired from the compression found from recent machine learning tools has emerged as a promising avenue for progress, with a broad range of applicability. This provides a surrogate model of the wave function with a far smaller number of parameters than the intractable number needed for a full description.

However, careful design of the surrogate model has important consequences in terms of the accuracy of the approximation and the efficiency of the optimization procedure. In this work we look under the hood at a particular class of these machine learning inspired states known as autoregressive models, which have been recently popularized by their success in image recognition, and advantageous sampling properties. We show how more general classes of states can inherit this property, and disentangle how different design choices affect the performance of these models.

Through our analysis and application to the ground states of a range of quantum many-body problems, we find that there is a cost to pay for the autoregressive property in terms of its ultimate flexibility in describing these states with a fixed number of parameters. With our work we hope to shine a light on important design choices required for the development of ever more powerful surrogate models for the wave function of interacting quantum particles.

► BibTeX data

@article{Bortone2024impactofconditional, doi = {10.22331/q-2024-02-08-1245}, url = {https://doi.org/10.22331/q-2024-02-08-1245}, title = {Impact of conditional modelling for a universal autoregressive quantum state}, author = {Bortone, Massimo and Rath, Yannic and Booth, George H.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{“{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {8}, pages = {1245}, month = feb, year = {2024}<br /> }

► References

[1] Daniel P. Arovas, Erez Berg, Steven Kivelson, and Srinivas Raghu. The Hubbard Model. Annual Review of Condensed Matter Physics, 13 (1): 239–274, March 2022. ISSN 1947-5454, 1947-5462. 10.1146/annurev-conmatphys-031620-102024.
https://doi.org/10.1146/annurev-conmatphys-031620-102024

[2] Thomas D. Barrett, Aleksei Malyshev, and A. I. Lvovsky. Autoregressive neural-network wavefunctions for ab initio quantum chemistry. Nature Machine Intelligence, 4 (4): 351–358, April 2022. ISSN 2522-5839. 10.1038/s42256-022-00461-z.
https://doi.org/10.1038/s42256-022-00461-z

[3] Sam Bond-Taylor, Adam Leach, Yang Long, and Chris G. Willcocks. Deep Generative Modelling: A Comparative Review of VAEs, GANs, Normalizing Flows, Energy-Based and Autoregressive Models. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44 (11): 7327–7347, November 2022. ISSN 1939-3539. 10.1109/TPAMI.2021.3116668.
https://doi.org/10.1109/TPAMI.2021.3116668

[4] Artem Borin and Dmitry A. Abanin. Approximating power of machine-learning ansatz for quantum many-body states. Physical Review B, 101 (19): 195141, May 2020. 10.1103/PhysRevB.101.195141.
https://doi.org/10.1103/PhysRevB.101.195141

[5] Sergey Bravyi, Giuseppe Carleo, David Gosset, and Yinchen Liu. A rapidly mixing Markov chain from any gapped quantum many-body system. Quantum, 7: 1173, November 2023. 10.22331/q-2023-11-07-1173.
https://doi.org/10.22331/q-2023-11-07-1173

[6] Marin Bukov, Markus Schmitt, and Maxime Dupont. Learning the ground state of a non-stoquastic quantum Hamiltonian in a rugged neural network landscape. SciPost Physics, 10 (6): 147, June 2021. ISSN 2542-4653. 10.21468/SciPostPhys.10.6.147.
https://doi.org/10.21468/SciPostPhys.10.6.147

[7] Giuseppe Carleo and Matthias Troyer. Solving the quantum many-body problem with artificial neural networks. Science, 355 (6325): 602–606, February 2017. 10.1126/science.aag2302.
https://doi.org/10.1126/science.aag2302

[8] Giuseppe Carleo, Kenny Choo, Damian Hofmann, James E. T. Smith, Tom Westerhout, Fabien Alet, Emily J. Davis, Stavros Efthymiou, Ivan Glasser, Sheng-Hsuan Lin, Marta Mauri, Guglielmo Mazzola, Christian B. Mendl, Evert van Nieuwenburg, Ossian O’Reilly, Hugo Théveniaut, Giacomo Torlai, Filippo Vicentini, and Alexander Wietek. NetKet: A machine learning toolkit for many-body quantum systems. SoftwareX, 10: 100311, July 2019. ISSN 2352-7110. 10.1016/j.softx.2019.100311.
https://doi.org/10.1016/j.softx.2019.100311

[9] Juan Carrasquilla, Giacomo Torlai, Roger G. Melko, and Leandro Aolita. Reconstructing quantum states with generative models. Nature Machine Intelligence, 1 (3): 155–161, March 2019. ISSN 2522-5839. 10.1038/s42256-019-0028-1.
https://doi.org/10.1038/s42256-019-0028-1

[10] Giovanni Cataldi, Ashkan Abedi, Giuseppe Magnifico, Simone Notarnicola, Nicola Dalla Pozza, Vittorio Giovannetti, and Simone Montangero. Hilbert curve vs Hilbert space: Exploiting fractal 2D covering to increase tensor network efficiency. Quantum, 5: 556, September 2021. 10.22331/q-2021-09-29-556.
https://doi.org/10.22331/q-2021-09-29-556

[11] Ao Chen and Markus Heyl. Efficient optimization of deep neural quantum states toward machine precision, February 2023.
arXiv:2302.01941

[12] Zhuo Chen, Laker Newhouse, Eddie Chen, Di Luo, and Marin Soljacic. ANTN: Bridging Autoregressive Neural Networks and Tensor Networks for Quantum Many-Body Simulation. In Thirty-Seventh Conference on Neural Information Processing Systems, November 2023.

[13] Kenny Choo, Titus Neupert, and Giuseppe Carleo. Two-dimensional frustrated $J_{1}-J_{2}$ model studied with neural network quantum states. Physical Review B, 100 (12): 125124, September 2019. 10.1103/PhysRevB.100.125124.
https://doi.org/10.1103/PhysRevB.100.125124

[14] Kenny Choo, Antonio Mezzacapo, and Giuseppe Carleo. Fermionic neural-network states for ab-initio electronic structure. Nature Communications, 11 (1): 2368, May 2020. ISSN 2041-1723. 10.1038/s41467-020-15724-9.
https://doi.org/10.1038/s41467-020-15724-9

[15] Stephen R. Clark. Unifying neural-network quantum states and correlator product states via tensor networks. Journal of Physics A: Mathematical and Theoretical, 51 (13): 135301, February 2018. ISSN 1751-8121. 10.1088/1751-8121/aaaaf2.
https://doi.org/10.1088/1751-8121/aaaaf2

[16] Dong-Ling Deng, Xiaopeng Li, and S. Das Sarma. Quantum Entanglement in Neural Network States. Physical Review X, 7 (2): 021021, May 2017. 10.1103/PhysRevX.7.021021.
https://doi.org/10.1103/PhysRevX.7.021021

[17] Kaelan Donatella, Zakari Denis, Alexandre Le Boité, and Cristiano Ciuti. Dynamics with autoregressive neural quantum states: Application to critical quench dynamics. Physical Review A, 108 (2): 022210, August 2023. 10.1103/PhysRevA.108.022210.
https://doi.org/10.1103/PhysRevA.108.022210

[18] J. Eisert, M. Cramer, and M. B. Plenio. Area laws for the entanglement entropy. Reviews of Modern Physics, 82 (1): 277–306, February 2010. 10.1103/RevModPhys.82.277.
https://doi.org/10.1103/RevModPhys.82.277

[19] J. M. Foster and S. F. Boys. Canonical Configurational Interaction Procedure. Reviews of Modern Physics, 32 (2): 300–302, April 1960. 10.1103/RevModPhys.32.300.
https://doi.org/10.1103/RevModPhys.32.300

[20] Clemens Giuliani, Filippo Vicentini, Riccardo Rossi, and Giuseppe Carleo. Learning ground states of gapped quantum Hamiltonians with Kernel Methods. Quantum, 7: 1096, August 2023. 10.22331/q-2023-08-29-1096.
https://doi.org/10.22331/q-2023-08-29-1096

[21] Aldo Glielmo, Yannic Rath, Gábor Csányi, Alessandro De Vita, and George H. Booth. Gaussian Process States: A Data-Driven Representation of Quantum Many-Body Physics. Physical Review X, 10 (4): 041026, November 2020. 10.1103/PhysRevX.10.041026.
https://doi.org/10.1103/PhysRevX.10.041026

[22] Johannes Hachmann, Wim Cardoen, and Garnet Kin-Lic Chan. Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group. The Journal of Chemical Physics, 125 (14): 144101, October 2006. ISSN 0021-9606. 10.1063/1.2345196.
https://doi.org/10.1063/1.2345196

[23] Jan Hermann, Zeno Schätzle, and Frank Noé. Deep-neural-network solution of the electronic Schrödinger equation. Nature Chemistry, 12 (10): 891–897, October 2020. ISSN 1755-4349. 10.1038/s41557-020-0544-y.
https://doi.org/10.1038/s41557-020-0544-y

[24] Jan Hermann, James Spencer, Kenny Choo, Antonio Mezzacapo, W. M. C. Foulkes, David Pfau, Giuseppe Carleo, and Frank Noé. Ab initio quantum chemistry with neural-network wavefunctions. Nature Reviews Chemistry, 7 (10): 692–709, October 2023. ISSN 2397-3358. 10.1038/s41570-023-00516-8.
https://doi.org/10.1038/s41570-023-00516-8

[25] Mohamed Hibat-Allah, Martin Ganahl, Lauren E. Hayward, Roger G. Melko, and Juan Carrasquilla. Recurrent neural network wave functions. Physical Review Research, 2 (2): 023358, June 2020. 10.1103/PhysRevResearch.2.023358.
https://doi.org/10.1103/PhysRevResearch.2.023358

[26] Mohamed Hibat-Allah, Roger G. Melko, and Juan Carrasquilla. Supplementing Recurrent Neural Network Wave Functions with Symmetry and Annealing to Improve Accuracy, July 2022.

[27] Mohamed Hibat-Allah, Roger G. Melko, and Juan Carrasquilla. Investigating topological order using recurrent neural networks. Physical Review B, 108 (7): 075152, August 2023. 10.1103/PhysRevB.108.075152.
https://doi.org/10.1103/PhysRevB.108.075152

[28] Hinton, Geoffrey, Srivastava, Nitish, and Swersky, Kevin. Lecture 6a: Overview of mini-batch gradient descent, 2012.

[29] Damian Hofmann, Giammarco Fabiani, Johan Mentink, Giuseppe Carleo, and Michael Sentef. Role of stochastic noise and generalization error in the time propagation of neural-network quantum states. SciPost Physics, 12 (5): 165, May 2022. ISSN 2542-4653. 10.21468/SciPostPhys.12.5.165.
https://doi.org/10.21468/SciPostPhys.12.5.165

[30] Bjarni Jónsson, Bela Bauer, and Giuseppe Carleo. Neural-network states for the classical simulation of quantum computing, August 2018.

[31] Diederik P. Kingma and Jimmy Ba. Adam: A Method for Stochastic Optimization, January 2017.

[32] King’s College London e-Research team. King’s Computational Research, Engineering and Technology Environment (CREATE), 2022. URL https://doi.org/10.18742/rnvf-m076.
https://doi.org/10.18742/rnvf-m076

[33] Dmitrii Kochkov and Bryan K. Clark. Variational optimization in the AI era: Computational Graph States and Supervised Wave-function Optimization. arXiv:1811.12423 [cond-mat, physics:physics], November 2018.
arXiv:1811.12423

[34] Chu-Cheng Lin, Aaron Jaech, Xin Li, Matthew R. Gormley, and Jason Eisner. Limitations of Autoregressive Models and Their Alternatives. In Proceedings of the 2021 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, pages 5147–5173, Online, June 2021. Association for Computational Linguistics. 10.18653/v1/2021.naacl-main.405.
https://doi.org/10.18653/v1/2021.naacl-main.405

[35] Sheng-Hsuan Lin and Frank Pollmann. Scaling of Neural-Network Quantum States for Time Evolution. physica status solidi (b), 259 (5): 2100172, 2022. ISSN 1521-3951. 10.1002/pssb.202100172.
https://doi.org/10.1002/pssb.202100172

[36] Alessandro Lovato, Corey Adams, Giuseppe Carleo, and Noemi Rocco. Hidden-nucleons neural-network quantum states for the nuclear many-body problem. Physical Review Research, 4 (4): 043178, December 2022. 10.1103/PhysRevResearch.4.043178.
https://doi.org/10.1103/PhysRevResearch.4.043178

[37] Di Luo, Zhuo Chen, Juan Carrasquilla, and Bryan K. Clark. Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation. Physical Review Letters, 128 (9): 090501, February 2022. 10.1103/PhysRevLett.128.090501.
https://doi.org/10.1103/PhysRevLett.128.090501

[38] Di Luo, Zhuo Chen, Kaiwen Hu, Zhizhen Zhao, Vera Mikyoung Hur, and Bryan K. Clark. Gauge-invariant and anyonic-symmetric autoregressive neural network for quantum lattice models. Physical Review Research, 5 (1): 013216, March 2023. 10.1103/PhysRevResearch.5.013216.
https://doi.org/10.1103/PhysRevResearch.5.013216

[39] Aleksei Malyshev, Juan Miguel Arrazola, and A. I. Lvovsky. Autoregressive Neural Quantum States with Quantum Number Symmetries, October 2023.

[40] Matija Medvidović and Giuseppe Carleo. Classical variational simulation of the Quantum Approximate Optimization Algorithm. npj Quantum Information, 7 (1): 1–7, June 2021. ISSN 2056-6387. 10.1038/s41534-021-00440-z.
https://doi.org/10.1038/s41534-021-00440-z

[41] Yusuke Nomura. Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry. Journal of Physics: Condensed Matter, 33 (17): 174003, April 2021. ISSN 0953-8984. 10.1088/1361-648X/abe268.
https://doi.org/10.1088/1361-648X/abe268

[42] Yusuke Nomura and Masatoshi Imada. Dirac-Type Nodal Spin Liquid Revealed by Refined Quantum Many-Body Solver Using Neural-Network Wave Function, Correlation Ratio, and Level Spectroscopy. Physical Review X, 11 (3): 031034, August 2021. 10.1103/PhysRevX.11.031034.
https://doi.org/10.1103/PhysRevX.11.031034

[43] David Pfau, James S. Spencer, Alexander G. D. G. Matthews, and W. M. C. Foulkes. Ab initio solution of the many-electron Schrödinger equation with deep neural networks. Physical Review Research, 2 (3): 033429, September 2020. 10.1103/PhysRevResearch.2.033429.
https://doi.org/10.1103/PhysRevResearch.2.033429

[44] Yannic Rath and George H. Booth. Quantum Gaussian process state: A kernel-inspired state with quantum support data. Physical Review Research, 4 (2): 023126, May 2022. 10.1103/PhysRevResearch.4.023126.
https://doi.org/10.1103/PhysRevResearch.4.023126

[45] Yannic Rath and George H. Booth. Framework for efficient ab initio electronic structure with Gaussian Process States. Physical Review B, 107 (20): 205119, May 2023. 10.1103/PhysRevB.107.205119.
https://doi.org/10.1103/PhysRevB.107.205119

[46] Yannic Rath, Aldo Glielmo, and George H. Booth. A Bayesian inference framework for compression and prediction of quantum states. The Journal of Chemical Physics, 153 (12): 124108, September 2020. ISSN 0021-9606. 10.1063/5.0024570.
https://doi.org/10.1063/5.0024570

[47] Waseem Rawat and Zenghui Wang. Deep Convolutional Neural Networks for Image Classification: A Comprehensive Review. Neural Computation, 29 (9): 2352–2449, September 2017. ISSN 0899-7667. 10.1162/neco_a_00990.
https://doi.org/10.1162/neco_a_00990

[48] Moritz Reh, Markus Schmitt, and Martin Gärttner. Optimizing design choices for neural quantum states. Physical Review B, 107 (19): 195115, May 2023. 10.1103/PhysRevB.107.195115.
https://doi.org/10.1103/PhysRevB.107.195115

[49] Christopher Roth and Allan H. MacDonald. Group Convolutional Neural Networks Improve Quantum State Accuracy, May 2021.

[50] Christopher Roth, Attila Szabó, and Allan H. MacDonald. High-accuracy variational Monte Carlo for frustrated magnets with deep neural networks. Physical Review B, 108 (5): 054410, August 2023. 10.1103/PhysRevB.108.054410.
https://doi.org/10.1103/PhysRevB.108.054410

[51] Anders W. Sandvik. Finite-size scaling of the ground-state parameters of the two-dimensional Heisenberg model. Physical Review B, 56 (18): 11678–11690, November 1997. 10.1103/PhysRevB.56.11678.
https://doi.org/10.1103/PhysRevB.56.11678

[52] H. J. Schulz, T. A. L. Ziman, and D. Poilblanc. Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions. Journal de Physique I, 6 (5): 675–703, May 1996. ISSN 1155-4304, 1286-4862. 10.1051/jp1:1996236.
https://doi.org/10.1051/jp1:1996236

[53] Or Sharir, Yoav Levine, Noam Wies, Giuseppe Carleo, and Amnon Shashua. Deep Autoregressive Models for the Efficient Variational Simulation of Many-Body Quantum Systems. Physical Review Letters, 124 (2): 020503, January 2020. 10.1103/PhysRevLett.124.020503.
https://doi.org/10.1103/PhysRevLett.124.020503

[54] Simons Collaboration on the Many-Electron Problem, Mario Motta, David M. Ceperley, Garnet Kin-Lic Chan, John A. Gomez, Emanuel Gull, Sheng Guo, Carlos A. Jiménez-Hoyos, Tran Nguyen Lan, Jia Li, Fengjie Ma, Andrew J. Millis, Nikolay V. Prokof’ev, Ushnish Ray, Gustavo E. Scuseria, Sandro Sorella, Edwin M. Stoudenmire, Qiming Sun, Igor S. Tupitsyn, Steven R. White, Dominika Zgid, and Shiwei Zhang. Towards the Solution of the Many-Electron Problem in Real Materials: Equation of State of the Hydrogen Chain with State-of-the-Art Many-Body Methods. Physical Review X, 7 (3): 031059, September 2017. 10.1103/PhysRevX.7.031059.
https://doi.org/10.1103/PhysRevX.7.031059

[55] Alessandro Sinibaldi, Clemens Giuliani, Giuseppe Carleo, and Filippo Vicentini. Unbiasing time-dependent Variational Monte Carlo by projected quantum evolution. Quantum, 7: 1131, October 2023. 10.22331/q-2023-10-10-1131.
https://doi.org/10.22331/q-2023-10-10-1131

[56] Anton V. Sinitskiy, Loren Greenman, and David A. Mazziotti. Strong correlation in hydrogen chains and lattices using the variational two-electron reduced density matrix method. The Journal of Chemical Physics, 133 (1): 014104, July 2010. ISSN 0021-9606. 10.1063/1.3459059.
https://doi.org/10.1063/1.3459059

[57] Sandro Sorella. Generalized Lanczos algorithm for variational quantum Monte Carlo. Physical Review B, 64 (2): 024512, June 2001. 10.1103/PhysRevB.64.024512.
https://doi.org/10.1103/PhysRevB.64.024512

[58] Lorenzo Stella, Claudio Attaccalite, Sandro Sorella, and Angel Rubio. Strong electronic correlation in the hydrogen chain: A variational Monte Carlo study. Physical Review B, 84 (24): 245117, December 2011. 10.1103/PhysRevB.84.245117.
https://doi.org/10.1103/PhysRevB.84.245117

[59] Qiming Sun, Timothy C. Berkelbach, Nick S. Blunt, George H. Booth, Sheng Guo, Zhendong Li, Junzi Liu, James D. McClain, Elvira R. Sayfutyarova, Sandeep Sharma, Sebastian Wouters, and Garnet Kin-Lic Chan. PySCF: The Python-based simulations of chemistry framework. WIREs Computational Molecular Science, 8 (1): e1340, 2018. ISSN 1759-0884. 10.1002/wcms.1340.
https://doi.org/10.1002/wcms.1340

[60] Qiming Sun, Xing Zhang, Samragni Banerjee, Peng Bao, Marc Barbry, Nick S. Blunt, Nikolay A. Bogdanov, George H. Booth, Jia Chen, Zhi-Hao Cui, Janus J. Eriksen, Yang Gao, Sheng Guo, Jan Hermann, Matthew R. Hermes, Kevin Koh, Peter Koval, Susi Lehtola, Zhendong Li, Junzi Liu, Narbe Mardirossian, James D. McClain, Mario Motta, Bastien Mussard, Hung Q. Pham, Artem Pulkin, Wirawan Purwanto, Paul J. Robinson, Enrico Ronca, Elvira R. Sayfutyarova, Maximilian Scheurer, Henry F. Schurkus, James E. T. Smith, Chong Sun, Shi-Ning Sun, Shiv Upadhyay, Lucas K. Wagner, Xiao Wang, Alec White, James Daniel Whitfield, Mark J. Williamson, Sebastian Wouters, Jun Yang, Jason M. Yu, Tianyu Zhu, Timothy C. Berkelbach, Sandeep Sharma, Alexander Yu. Sokolov, and Garnet Kin-Lic Chan. Recent developments in the PySCF program package. The Journal of Chemical Physics, 153 (2): 024109, July 2020. ISSN 0021-9606. 10.1063/5.0006074.
https://doi.org/10.1063/5.0006074

[61] Xiao-Qi Sun, Tamra Nebabu, Xizhi Han, Michael O. Flynn, and Xiao-Liang Qi. Entanglement features of random neural network quantum states. Physical Review B, 106 (11): 115138, September 2022. 10.1103/PhysRevB.106.115138.
https://doi.org/10.1103/PhysRevB.106.115138

[62] Attila Szabó and Claudio Castelnovo. Neural network wave functions and the sign problem. Physical Review Research, 2 (3): 033075, July 2020. 10.1103/PhysRevResearch.2.033075.
https://doi.org/10.1103/PhysRevResearch.2.033075

[63] Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer, Roger Melko, and Giuseppe Carleo. Neural-network quantum state tomography. Nature Physics, 14 (5): 447–450, May 2018. ISSN 1745-2481. 10.1038/s41567-018-0048-5.
https://doi.org/10.1038/s41567-018-0048-5

[64] Takashi Tsuchimochi and Gustavo E. Scuseria. Strong correlations via constrained-pairing mean-field theory. The Journal of Chemical Physics, 131 (12): 121102, September 2009. ISSN 0021-9606. 10.1063/1.3237029.
https://doi.org/10.1063/1.3237029

[65] Benigno Uria, Marc-Alexandre Côté, Karol Gregor, Iain Murray, and Hugo Larochelle. Neural Autoregressive Distribution Estimation. Journal of Machine Learning Research, 17 (205): 1–37, 2016. ISSN 1533-7928.

[66] Aaron van den Oord, Nal Kalchbrenner, Lasse Espeholt, koray kavukcuoglu, Oriol Vinyals, and Alex Graves. Conditional Image Generation with PixelCNN Decoders. In Advances in Neural Information Processing Systems, volume 29. Curran Associates, Inc., 2016.

[67] Filippo Vicentini, Damian Hofmann, Attila Szabó, Dian Wu, Christopher Roth, Clemens Giuliani, Gabriel Pescia, Jannes Nys, Vladimir Vargas-Calderón, Nikita Astrakhantsev, and Giuseppe Carleo. NetKet 3: Machine Learning Toolbox for Many-Body Quantum Systems. SciPost Physics Codebases, page 007, August 2022. ISSN 2949-804X. 10.21468/SciPostPhysCodeb.7.
https://doi.org/10.21468/SciPostPhysCodeb.7

[68] Tom Vieijra, Corneel Casert, Jannes Nys, Wesley De Neve, Jutho Haegeman, Jan Ryckebusch, and Frank Verstraete. Restricted Boltzmann Machines for Quantum States with Non-Abelian or Anyonic Symmetries. Physical Review Letters, 124 (9): 097201, March 2020. 10.1103/PhysRevLett.124.097201.
https://doi.org/10.1103/PhysRevLett.124.097201

[69] Luciano Loris Viteritti, Riccardo Rende, and Federico Becca. Transformer Variational Wave Functions for Frustrated Quantum Spin Systems. Physical Review Letters, 130 (23): 236401, June 2023. 10.1103/PhysRevLett.130.236401.
https://doi.org/10.1103/PhysRevLett.130.236401

[70] Yezhen Wang, Tong Che, Bo Li, Kaitao Song, Hengzhi Pei, Yoshua Bengio, and Dongsheng Li. Your Autoregressive Generative Model Can be Better If You Treat It as an Energy-Based One, June 2022.

[71] Tom Westerhout, Nikita Astrakhantsev, Konstantin S. Tikhonov, Mikhail I. Katsnelson, and Andrey A. Bagrov. Generalization properties of neural network approximations to frustrated magnet ground states. Nature Communications, 11 (1): 1593, March 2020. ISSN 2041-1723. 10.1038/s41467-020-15402-w.
https://doi.org/10.1038/s41467-020-15402-w

[72] Dian Wu, Riccardo Rossi, Filippo Vicentini, and Giuseppe Carleo. From tensor-network quantum states to tensorial recurrent neural networks. Physical Review Research, 5 (3): L032001, July 2023. 10.1103/PhysRevResearch.5.L032001.
https://doi.org/10.1103/PhysRevResearch.5.L032001

[73] Huanchen Zhai and Garnet Kin-Lic Chan. Low communication high performance ab initio density matrix renormalization group algorithms. The Journal of Chemical Physics, 154 (22): 224116, June 2021. ISSN 0021-9606. 10.1063/5.0050902.
https://doi.org/10.1063/5.0050902

[74] Yuan-Hang Zhang and Massimiliano Di Ventra. Transformer quantum state: A multipurpose model for quantum many-body problems. Physical Review B, 107 (7): 075147, February 2023. 10.1103/PhysRevB.107.075147.
https://doi.org/10.1103/PhysRevB.107.075147

[75] Tianchen Zhao, Saibal De, Brian Chen, James Stokes, and Shravan Veerapaneni. Overcoming barriers to scalability in variational quantum Monte Carlo. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, SC ’21, pages 1–13, New York, NY, USA, November 2021. Association for Computing Machinery. ISBN 978-1-4503-8442-1. 10.1145/3458817.3476219.
https://doi.org/10.1145/3458817.3476219

[76] Tianchen Zhao, James Stokes, and Shravan Veerapaneni. Scalable neural quantum states architecture for quantum chemistry. Machine Learning: Science and Technology, 4 (2): 025034, June 2023. ISSN 2632-2153. 10.1088/2632-2153/acdb2f.
https://doi.org/10.1088/2632-2153/acdb2f

[77] Ding-Xuan Zhou. Universality of deep convolutional neural networks. Applied and Computational Harmonic Analysis, 48 (2): 787–794, March 2020. ISSN 1063-5203. 10.1016/j.acha.2019.06.004.
https://doi.org/10.1016/j.acha.2019.06.004

Cited by

Could not fetch Crossref cited-by data during last attempt 2024-02-08 12:50:38: Could not fetch cited-by data for 10.22331/q-2024-02-08-1245 from Crossref. This is normal if the DOI was registered recently. On SAO/NASA ADS no data on citing works was found (last attempt 2024-02-08 12:50:38).

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.

SEO Powered Content & PR Distribution. Get Amplified Today.
PlatoData.Network Vertical Generative Ai. Empower Yourself. Access Here.
PlatoAiStream. Web3 Intelligence. Knowledge Amplified. Access Here.
PlatoESG. Carbon, CleanTech, Energy, Environment, Solar, Waste Management. Access Here.
PlatoHealth. Biotech and Clinical Trials Intelligence. Access Here.
Source: https://quantum-journal.org/papers/q-2024-02-08-1245/

Generative Data Intelligence

Impact of conditional modelling for a universal autoregressive quantum state

Abstract

Popular summary

► BibTeX data

► References

Cited by

Drake Threatened With Lawsuit Over Tupac AI Vocals

Shiba Inu Leads in Robinhood’s Crypto Performance

Latest Intelligence

DOJ Disputes Roman Storm’s Characterization of Tornado Cash Operations in New Filing

Top 5 Crypto Presales: BDAG Leads the Pack with 30,000x ROI Potential

Forbes Unveils 20 Crypto ‘Zombies,’ Declares Ripple And XRP Among The Undead

Consob, Italy’s Watchdog, Bans Additional Forex And Cryptocurrency Trading Websites – CryptoInfoNet

Fed’s Inflation Gauge Heats Up, Rate Cuts on Hold as Bitcoin and Stocks Slide

Explore Top 6 Cryptos for 2024: BlockDAG Leads with Unprecedented ROI Potential

Chat with us