Investigating topological order using recurrent neural networks
Open accessAbstract
Recurrent neural networks (RNNs), originally developed for natural language processing, hold great promise for accurately describing strongly correlated quantum many-body systems. Here, we employ two-dimensional RNNs to investigate two prototypical quantum many-body Hamiltonians exhibiting topological order. Specifically, we demonstrate that RNN wave functions can effectively capture the topological order of the toric code and a Bose-Hubbard spin liquid on the kagome lattice by estimating their topological entanglement entropies. We also find that RNNs favor coherent superpositions of minimally entangled states over minimally entangled states themselves. Overall, our findings demonstrate that RNN wave functions constitute a powerful tool to study phases of matter beyond Landau's symmetry-breaking paradigm.
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Cites
Hochreiter, S., & Schmidhuber, J. (1997) · Neural Computation · doi:10.1162/neco.1997.9.8.1735 · Cited by 102,318 · see citing works
Harris, C. R., Millman, K. J., van der Walt, S. J., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N. J., et al. (2020) · Nature · doi:10.1038/s41586-020-2649-2 · Cited by 23,826 · see citing works
Harris, C., Millman, K., van der Walt, S., Gommers, R., Virtanen, P., Cournapeau, D., Wieser, E., Taylor, J., Berg, S., Smith, N., et al. (2020) · RePEc: Research Papers in Economics · Cited by 17,844 · see citing works
Anyons in an exactly solved model and beyond
Kitaev, A. (2006) · Annals of Physics · doi:10.1016/j.aop.2005.10.005 · Cited by 5,245 · see citing works
Advances in neural information processing systems 11
Peter Sollich, A. (1999) · Cited by 3,168 · see citing works
Supervised Sequence Labelling with Recurrent Neural Networks
Graves, A. (2012) · Studies in Computational Intelligence · doi:10.1007/978-3-642-24797-2 · Cited by 3,120 · see citing works
Sachdev, S. (2011) · doi:10.1017/cbo9780511973765 · Cited by 2,842 · see citing works
A Critical Review of Recurrent Neural Networks for Sequence LearningPreprint
Lipton, Z. C., Berkowitz, J. A., & Elkan, C. (2015) · arXiv (Cornell University) · doi:10.48550/arxiv.1506.00019 · Cited by 2,711 · see citing works
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 2,453 · see citing works
Topological Entanglement Entropy
Kitaev, A., & Preskill, J. P. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.110404 · Cited by 2,409 · see citing works
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 · see citing works
Detecting Topological Order in a Ground State Wave Function
Levin, M., & Wen, X.-G. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.110405 · Cited by 2,084 · see citing works
Dennis, E., Kitaev, A., Landahl, A., & Preskill, J. (2002) · Journal of Mathematical Physics · doi:10.1063/1.1499754 · Cited by 1,768 · see citing works
Dennis, E., Kitaev, A., Landahl, A., & Preskill, J. (2001) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,485 · see citing works
Machine learning phases of matter
Carrasquilla, J., & Melko, R. G. (2017) · Nature Physics · doi:10.1038/nphys4035 · Cited by 1,448 · see citing works
Self-citationField Theories of Condensed Matter Physics
Fradkin, E. (2013) · Cambridge University Press eBooks · doi:10.1017/cbo9781139015509 · Cited by 1,191 · see citing works
Machine learning & artificial intelligence in the quantum domain: a review of recent progress
Dunjko, V., & Briegel, H. J. (2018) · Reports on Progress in Physics · doi:10.1088/1361-6633/aab406 · Cited by 1,132 · see citing works
Suppressing quantum errors by scaling a surface code logical qubit
Google Quantum, A. I., Acharya, R., Aleiner, I., Allen, R., Andersen, T. I., Ansmann, M., Arute, F., Arya, K., Asfaw, A., Atalaya, J., et al. (2023) · Nature · doi:10.1038/s41586-022-05434-1 · Cited by 1,103 · cited 2× · see citing works
“[8] Rajeev Acharya, Igor Aleiner, Richard Allen, Trond I.”
BackgroundProceedings of the 26th Conference on Uncertainty in Artificial Intelligence (UAI 2010)
Adams, R. P., Dahl, G. E., & Murray, I. (2010) · Cited by 943 · see citing works
Neural-network quantum state tomography
Torlai, G., Mazzola, G., Carrasquilla, J., Troyer, M., Melko, R. G., & Carleo, G. (2018) · Nature Physics · doi:10.1038/s41567-018-0048-5 · Cited by 855 · see citing works
Self-citationProbing topological spin liquids on a programmable quantum simulator
Semeghini, G., Levine, H., Keesling, A., Ebadi, S., Wang, T. T., Bluvstein, D., Verresen, R., Pichler, H., Kalinowski, M., Samajdar, R., et al. (2021) · Science · doi:10.1126/science.abi8794 · Cited by 781 · see citing works
Realizing repeated quantum error correction in a distance-three surface code
Krinner, S., Lacroix, N., Remm, A., Di Paolo, A., Genois, E., Leroux, C., Hellings, C., Lazar, S., Swiadek, F., Herrmann, J., et al. (2022) · Nature · doi:10.1038/s41586-022-04566-8 · Cited by 686 · see citing works
Identifying topological order by entanglement entropy
Jiang, H., Wang, Z., & Balents, L. (2012) · Nature Physics · doi:10.1038/nphys2465 · Cited by 633 · see citing works
Deep-neural-network solution of the electronic Schrödinger equation
Hermann, J., Schätzle, Z., & Noé, F. (2020) · Nature Chemistry · doi:10.1038/s41557-020-0544-y · Cited by 559 · see citing works
Ab initio solution of the many-electron Schrödinger equation with deep neural networks
Pfau, D., Spencer, J. S., Matthews, A. G. D. G., & Foulkes, W. M. C. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033429 · Cited by 555 · see citing works
Quantum Monte Carlo Approaches for Correlated Systems
Becca, F., & Sorella, S. (2017) · doi:10.1017/9781316417041 · Cited by 523 · see citing works
Studying Two-Dimensional Systems with the Density Matrix Renormalization Group
Stoudenmire, E. M., & White, S. R. (2012) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-020911-125018 · Cited by 451 · see citing works
Realizing topologically ordered states on a quantum processor
Satzinger, K. J., Liu, Y.-J., Smith, A., Knapp, C., Newman, M., Jones, C., Chen, Z., Quintana, C., Mi, X., Dunsworth, A., et al. (2021) · Repository@Nottingham (University of Nottingham) · doi:10.5281/zenodo.5570481 · Cited by 424 · see citing works
Measuring Renyi Entanglement Entropy in Quantum Monte Carlo Simulations
Hastings, M. B., González, I., Kallin, A. B., & Melko, R. G. (2010) · Physical Review Letters · doi:10.1103/physrevlett.104.157201 · Cited by 421 · see citing works
Self-citationReal-time quantum error correction beyond break-even
Sivak, V. V., Eickbusch, A., Royer, B., Singh, S., Tsioutsios, I., Ganjam, S., Miano, A., Brock, B. L., Ding, A. Z., Frunzio, L., et al. (2023) · Nature · doi:10.1038/s41586-023-05782-6 · Cited by 407 · see citing works
Machine learning quantum phases of matter beyond the fermion sign problem
Broecker, P., Carrasquilla, J., Melko, R. G., & Trebst, S. (2017) · Scientific Reports · doi:10.1038/s41598-017-09098-0 · Cited by 391 · see citing works
Self-citationMinimal gated unit for recurrent neural networks
Zhou, G., Wu, J., Zhang, C.-L., & Zhou, Z. (2016) · Machine Intelligence Research · doi:10.1007/s11633-016-1006-2 · Cited by 362 · see citing works
Quasiparticle statistics and braiding from ground-state entanglement
Zhang, Y., Grover, T., Turner, A. M., Oshikawa, M., & Vishwanath, A. (2012) · Physical Review B · doi:10.1103/physrevb.85.235151 · Cited by 343 · see citing works
Machine Learning Phases of Strongly Correlated Fermions
Ch’ng, K., Carrasquilla, J., Melko, R. G., & Khatami, E. (2017) · Physical Review X · doi:10.1103/physrevx.7.031038 · Cited by 333 · see citing works
Self-citationReconstructing quantum states with generative models
Carrasquilla, J., Torlai, G., Melko, R. G., & Aolita, L. (2019) · Nature Machine Intelligence · doi:10.1038/s42256-019-0028-1 · Cited by 321 · see citing works
Self-citationMulti-dimensional Recurrent Neural Networks
Graves, A., Fernández, S., & Schmidhuber, J. (2007) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-74690-4_56 · Cited by 303 · see citing works
Bipartite entanglement and entropic boundary law in lattice spin systems
Hamma, A., Ionicioiu, R., & Paolo Zanardi, A. (2005) · Physical Review A · doi:10.1103/physreva.71.022315 · Cited by 298 · see citing works
Machine learning topological states
Deng, D.-L., Li, X., & Sarma, S. D. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.96.195145 · Cited by 294 · see citing works
Plaquette Ordered Phase and Quantum Phase Diagram in the Spin- 12 J1−J2 Square Heisenberg Model
Gong, S.-S., Zhu, W. K., Sheng, D. N., Motrunich, O. I., & Fisher, M. P. A. (2014) · Physical Review Letters · doi:10.1103/physrevlett.113.027201 · Cited by 275 · see citing works
Recurrent neural network wave functions
Hibat-Allah, M., Ganahl, M., Hayward, L. E., Melko, R. G., & Carrasquilla, J. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.023358 · Cited by 274 · see citing works
Self-citationNeural-Network Quantum States, String-Bond States, and Chiral Topological States
Glasser, I., Pancotti, N., August, M., Rodriguez, I. D., & Cirac, J. I. (2018) · Physical Review X · doi:10.1103/physrevx.8.011006 · Cited by 273 · see citing works
Topological entanglement entropy of a Bose–Hubbard spin liquid
Isakov, S. V., Hastings, M. B., & Melko, R. G. (2011) · Nature Physics · doi:10.1038/nphys2036 · Cited by 264 · see citing works
Self-citationFermionic neural-network states for ab-initio electronic structure
Choo, K., Mezzacapo, A., & Carleo, G. (2020) · Nature Communications · doi:10.1038/s41467-020-15724-9 · Cited by 252 · see citing works
Ground state entanglement and geometric entropy in the Kitaev model
Hamma, A., Ionicioiu, R., & Paolo Zanardi, A. (2005) · Physics Letters A · doi:10.1016/j.physleta.2005.01.060 · Cited by 250 · see citing works
Neural-Network Quantum States, String-Bond States, and Chiral Topological States
Glasser, I., Pancotti, N., August, M., Rodríguez, I., & Cirac, J. I. (2018) · Max Planck Digital Library · Cited by 250 · see citing works
Topological Entanglement Rényi Entropy and Reduced Density Matrix Structure
Flammia, S. T., Hamma, A., Hughes, T. L., & Wen, X.-G. (2009) · Physical Review Letters · doi:10.1103/physrevlett.103.261601 · Cited by 248 · see citing works
Equivalence of restricted Boltzmann machines and tensor network states
Chen, J., Cheng, S., Xie, H., Wang, L., & Xiang, T. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.085104 · Cited by 245 · see citing works
Machine learning for quantum matter
Carrasquilla, J. (2020) · Advances in Physics X · doi:10.1080/23746149.2020.1797528 · Cited by 232 · see citing works
Self-citationApproximating quantum many-body wave functions using artificial neural networks
Cai, Z., & Liu, J.-G. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.97.035116 · Cited by 215 · see citing works
Variational Neural-Network Ansatz for Steady States in Open Quantum Systems
Vicentini, F., Biella, A., Regnault, N., & Ciuti, C. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.250503 · Cited by 213 · see citing works
Gradient methods for variational optimization of projected entangled-pair states
Vanderstraeten, L., Haegeman, J., Corboz, P., & Verstraete, F. (2016) · Physical Review B · doi:10.1103/physrevb.94.155123 · Cited by 206 · see citing works
Prediction of Toric Code Topological Order from Rydberg Blockade
Verresen, R., Lukin, M. D., & Vishwanath, A. (2021) · Physical Review X · doi:10.1103/physrevx.11.031005 · Cited by 206 · see citing works
Quantum phases of Rydberg atoms on a kagome lattice
Samajdar, R., Ho, W. W., Pichler, H., Lukin, M. D., & Subir Sachdev, A. (2021) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2015785118 · Cited by 191 · see citing works
Monte Carlo Gradient Estimation in Machine LearningPreprint
Mohamed, S., Rosca, M., Figurnov, M., & Mnih, A. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1906.10652 · Cited by 186 · see citing works
Wen, X.-G. (2013) · ISRN Condensed Matter Physics · doi:10.1155/2013/198710 · Cited by 183 · see citing works
Backflow Transformations via Neural Networks for Quantum Many-Body Wave Functions
Luo, D., & Clark, B. K. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.226401 · Cited by 174 · see citing works
Artificial neural network methods in quantum mechanics
Lagaris, I. E., Likas, A. C., & Fotiadis, D. I. (1997) · Computer Physics Communications · doi:10.1016/s0010-4655(97)00054-4 · Cited by 169 · see citing works
Topological entanglement entropy in the quantum dimer model on the triangular lattice
Furukawa, S., & Misguich, G. (2007) · Physical Review B · doi:10.1103/physrevb.75.214407 · Cited by 145 · see citing works
Perfect sampling with unitary tensor networks
Ferris, A. J., & Vidal, G. (2012) · Physical Review B · doi:10.1103/physrevb.85.165146 · Cited by 138 · see citing works
Helping restricted Boltzmann machines with quantum-state representation by restoring symmetry
Nomura, Y. (2021) · Journal of Physics Condensed Matter · doi:10.1088/1361-648x/abe268 · Cited by 88 · see citing works
Autoregressive Neural Network for Simulating Open Quantum Systems via a Probabilistic Formulation
Luo, D., Chen, Z., Carrasquilla, J., & Clark, B. K. (2022) · Physical Review Letters · doi:10.1103/physrevlett.128.090501 · Cited by 80 · see citing works
Self-citationClassical variational simulation of the Quantum Approximate Optimization Algorithm
Medvidović, M., & Carleo, G. (2021) · npj Quantum Information · doi:10.1038/s41534-021-00440-z · Cited by 79 · see citing works
Hibat-Allah, M., Inack, E. M., Wiersema, R., Melko, R. G., & Carrasquilla, J. (2021) · Nature Machine Intelligence · doi:10.1038/s42256-021-00401-3 · Cited by 79 · see citing works
Self-citationDynamical Preparation of Quantum Spin Liquids in Rydberg Atom Arrays
Giudici, G., Lukin, M. D., & Pichler, H. (2022) · Physical Review Letters · doi:10.1103/physrevlett.129.090401 · Cited by 76 · see citing works
Topological phases and quantum computationPreprint
Kitaev, A., & Laumann, C. R. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0904.2771 · Cited by 75 · see citing works
Bukov, M., Schmitt, M., & Dupont, M. (2021) · eScholarship (California Digital Library) · Cited by 73 · see citing works
Bukov, M., Schmitt, M., & Dupont, M. (2021) · SciPost Physics · doi:10.21468/scipostphys.10.6.147 · Cited by 66 · see citing works
Efficient representation of topologically ordered states with restricted Boltzmann machines
Lu, S., Gao, X., & Duan, L.-M. (2019) · Physical review. B./Physical review. B · doi:10.1103/physrevb.99.155136 · Cited by 66 · see citing works
Modern applications of machine learning in quantum sciencesPreprint
Dawid, A., Arnold, J., Requena, B., Gresch, A., Płodzień, M., Donatella, K., Nicoli, K. A., Stornati, P., Koch, R., Büttner, M., et al. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2204.04198 · Cited by 63 · see citing works
Self-citationContracting projected entangled pair states is average-case hard
Haferkamp, J., Hangleiter, D., Eisert, J., & Gluza, M. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.013010 · Cited by 62 · see citing works
Gauge-invariant and anyonic-symmetric autoregressive neural network for quantum lattice models
Luo, D., Chen, Z., Hu, K., Zhao, Z., Hur, V. M., & Clark, B. K. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.013216 · Cited by 62 · see citing works
Spin-Liquid Phase in a Spin- 1/2 Quantum Magnet on the Kagome Lattice
Isakov, S. V., Kim, Y. B., & Paramekanti, A. (2006) · Physical Review Letters · doi:10.1103/physrevlett.97.207204 · Cited by 61 · see citing works
Zhao, J., Chen, B.-B., Wang, Y.-C., Yan, Z., Cheng, M., & Meng, Z. Y. (2022) · npj Quantum Materials · doi:10.1038/s41535-022-00476-0 · Cited by 61 · see citing works
Neural-network states for the classical simulation of quantum computingPreprint
Jónsson, B., Bauer, B., & Carleo, G. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1808.05232 · Cited by 60 · see citing works
Neural Error Mitigation of Near-Term Quantum Simulations
Bennewitz, E. R., Hopfmueller, F., Kulchytskyy, B., Carrasquilla, J., & Ronagh, P. (2022) · Nature Machine Intelligence · doi:10.1038/s42256-022-00509-0 · Cited by 59 · see citing works
Self-citationHigh-accuracy variational Monte Carlo for frustrated magnets with deep neural networks
Roth, C., Szabó, A., & MacDonald, A. H. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.054410 · Cited by 58 · see citing works
Probabilistic simulation of quantum circuits using a deep-learning architecture
Carrasquilla, J., Luo, D., Pérez, F., Milsted, A., Clark, B. K., Volkovs, M., & Aolita, L. (2021) · Physical Review A · doi:10.1103/physreva.104.032610 · Cited by 53 · see citing works
Self-citationMulti-Dimensional Recurrent Neural NetworksPreprint
Graves, A., Fernandez, S., & Schmidhuber, J. (2007) · arXiv (Cornell University) · doi:10.48550/arxiv.0705.2011 · Cited by 48 · see citing works
Contracting projected entangled pair states is average-case hard
Haferkamp, J., Hangleiter, D., Eisert, J., & Gluza, M. (2020) · Refubium (Universitätsbibliothek der Freien Universität Berlin) · doi:10.17169/refubium-30079 · Cited by 44 · see citing works
Machine learning discovery of new phases in programmable quantum simulator snapshots
Miles, C., Samajdar, R., Ebadi, S., Wang, T. T., Pichler, H., Subir Sachdev, A., Lukin, M. D., Greiner, M., Weinberger, K. Q., & Kim, E.-A. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.013026 · Cited by 41 · see citing works
Detecting Goldstone modes with entanglement entropy
Kulchytskyy, B., Herdman, C. M., Inglis, S., & Melko, R. G. (2015) · Physical Review B · doi:10.1103/physrevb.92.115146 · Cited by 40 · see citing works
Self-citationFrom tensor-network quantum states to tensorial recurrent neural networks
Wu, D., Rossi, R., Vicentini, F., & Carleo, G. (2023) · Physical Review Research · doi:10.1103/physrevresearch.5.l032001 · Cited by 37 · see citing works
Iterative Retraining of Quantum Spin Models Using Recurrent Neural NetworksPreprint
Roth, C. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2003.06228 · Cited by 23 · see citing works
Data-enhanced variational Monte Carlo simulations for Rydberg atom arrays
Czischek, S., Moss, M. S., Radzihovsky, M., Merali, E., & Melko, R. G. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.105.205108 · Cited by 22 · see citing works
Self-citationCalculating Rényi entropies with neural autoregressive quantum states
Wang, Z., & Davis, E. J. (2020) · Physical Review A · doi:10.1103/physreva.102.062413 · Cited by 20 · see citing works
Casert, C., Vieijra, T., Whitelam, S., & Tamblyn, I. (2021) · Physical Review Letters · doi:10.1103/physrevlett.127.120602 · Cited by 20 · see citing works
Supplementing recurrent neural networks with annealing to solve combinatorial optimization problems
Khandoker, S. A., Abedin, J. M., & Hibat-Allah, M. (2023) · Machine Learning Science and Technology · doi:10.1088/2632-2153/acb895 · Cited by 15 · see citing works
Self-citationLocally Masked Convolution for Autoregressive ModelsPreprint
Jain, A., Abbeel, P., & Pathak, D. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2006.12486 · Cited by 15 · see citing works
Entanglement entropy and topological order in resonating valence-bond quantum spin liquids
Wildeboer, J., Seidel, A., & Melko, R. G. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.100402 · Cited by 14 · see citing works
Self-citationNeural network solution of the Schrödinger equation for a two-dimensional harmonic oscillator
Androsiuk, J., Kułak, L., & Sienicki, K. (1993) · Chemical Physics · doi:10.1016/0301-0104(93)80153-z · Cited by 14 · see citing works
Monte Carlo simulation of stoquastic HamiltoniansPreprint
Bravyi, S. B. (2014) · arXiv (Cornell University) · doi:10.48550/arxiv.1402.2295 · Cited by 13 · see citing works
TensorNetwork on TensorFlow: A Spin Chain Application Using Tree Tensor NetworksPreprint
Milsted, A., Ganahl, M., Leichenauer, S., et al. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.01331 · Cited by 12 · see citing works
Minimal Gated Unit for Recurrent Neural NetworksPreprint
Zhou, G., Wu, J., Zhang, C.-L., et al. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1603.09420 · Cited by 11 · see citing works
Topological Spin Liquid with Symmetry-Protected Edge StatesPreprint
Wang, Y.-C., Qi, Y., Cheng, M., et al. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1701.01552 · Cited by 11 · see citing works
Mutual Information Scaling and Expressive Power of Sequence ModelsPreprint
Shen, H. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1905.04271 · Cited by 7 · see citing works
High-accuracy variational Monte Carlo for frustrated magnets with deep neural networksPreprint
Roth, C., Szabó, A., & MacDonald, A. H. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2211.07749 · Cited by 4 · see citing works
Universal lower bound on topological entanglement entropy
Kim, I. H., Levin, M., Lin, T.-C., et al. (2023) · PubMed · doi:10.48550/arxiv.2302.00689 · Cited by 1 · see citing works
Collapsing Schrödinger Cats in the Density Matrix Renormalization GroupPreprint
Jiang, H., & Balents, L. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1309.7438
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Research works printed but not linked: 6
- K. J. Satzinger, Y.-J Liu, A. Smith, C. Knapp, M. Newman, C. Jones, Z. Chen, C. Quintana, X. Mi, A. Dunsworth, C. Gidney, I. Aleiner, F. Arute, K. Arya, J. Atalaya, R. Babbush, J. C. Bardin, R. Barends, J. Basso, A. Bengtsson, A. Bilmes, M. Broughton, B. B. Buckley, D. A. Buell, B. Burkett, N. Bushnell, B. Chiaro, R. Collins, W. Courtney, S. Demura, A. R. Derk, D. Ep- pens, C. Erickson, L. Faoro, E. Farhi, A. G. Fowler, B. Foxen, M. Giustina, A. Greene, J. A. Gross, M. P. Harrigan, S. D. Harrington, J. Hilton, S. Hong, T. Huang, W. J. Huggins, L. B. Ioffe, S. V. Isakov, E. Jeffrey, Z. Jiang, D. Kafri, K. Kechedzhi, T. Khattar, S. Kim, P. V. Klimov, A. N. Korotkov, F. Kostritsa, D. Land- huis, P. Laptev, A. Locharla, E. Lucero, O. Martin, J. R. McClean, M. McEwen, K. C. Miao, M. Mohseni, S. Mon- tazeri, W. Mruczkiewicz, J. Mutus, O. Naaman, M. Nee- ley, C. Neill, M. Y. Niu, T. E. O'Brien, A. Oprem- cak, B. Pató, A. Petukhov, N. C. Rubin, D. Sank, V. Shvarts, D. Strain, M. Szalay, B. Villalonga, T. C. White, Z. Yao, P. Yeh, J. Yoo, A. Zalcman, H. Neven, S. Boixo, A. Megrant, Y. Chen, J. Kelly, V. Smelyanskiy, A. Kitaev, M. Knap, F. Pollmann, and P. Roushan, "Re- alizing topologically ordered states on a quantum proces- sor," Science 374, 1237-1241 (2021). · DOI
- Di Luo, Zhuo Chen, Kaiwen Hu, Zhizhen Zhao, Vera Mikyoung Hur, and Bryan K. Clark, "Gauge in- variant autoregressive neural networks for quantum lat- tice models," (2021), arXiv:2101.07243 [cond-mat.str-el]. · arXiv
- Mohamed Hibat-Allah, Roger G Melko, and Juan Car- rasquilla, "Supplementing recurrent neural network wave functions with symmetry and annealing to improve ac- curacy," Machine Learning and the Physical Sciences (NeurIPS 2021) .
- Richard S Sutton, David A McAllester, Satinder P Singh, and Yishay Mansour, "Policy gradient methods for rein- forcement learning with function approximation," in Ad- vances in neural information processing systems (2000) pp. 1057-1063.
- Diederik P. Kingma and Jimmy Ba, "Adam: A method for stochastic optimization," in 3rd International Con- ference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Pro- ceedings, edited by Yoshua Bengio and Yann LeCun (2015).
- Harry H Ku et al., "Notes on the use of propagation of error formulas," Journal of Research of the National Bureau of Standards 70 (1966).
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- Authors
- Hibat-Allah, M., Melko, R. G., & Carrasquilla, J.
- Affiliations
- University of Waterloo (CA)
- Corresponding author
- Hibat-Allah, Mohamed
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2023-08-22
- Volume
- 108
- Issue
- 7
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W4386074054
- Cited by
- 27
- References
- 82
- Citations by year
- 2026: 3 · 2025: 13 · 2024: 11
- FWCI
- 3.14
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Natural Sciences and Engineering Research Council of Canada
- Shared Hierarchical Academic Research Computing Network
- Canadian Institute for Advanced Research
- Government of Canada
- Innovation, Science and Economic Development Canada
- Ministry of Colleges and Universities
- 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 › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- recurrent neural networks, topological order, toric code, Bose-Hubbard model, kagome lattice, spin liquid, topological entanglement entropy, entanglement entropy, quantum many-body systems, neural quantum states
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