Abstract
A key challenge in the effort to simulate todayâs quantum computing devices is the ability to learn and encode the complex correlations that occur between qubits. Emerging technologies based on language models adopted from machine learning have shown unique abilities to learn quantum states. We highlight the contributions that language models are making in the effort to build quantum computers and discuss their future role in the race to quantum advantage.
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References
Arute, F. et al. Quantum supremacy using a programmable superconducting processor. Nature 574, 505â510 (2019).
Zhong, H.-S. et al. Quantum computational advantage using photons. Science 370, 1460â1463 (2020).
Madsen, L. S. et al. Quantum computational advantage with a programmable photonic processor. Nature 606, 75â81 (2022).
Kim, Y. et al. Evidence for the utility of quantum computing before fault tolerance. Nature 618, 500â505 (2023).
Carrasquilla, J., Torlai, G., Melko, R. G. & Aolita, L. Reconstructing quantum states with generative models. Nat. Mach. Intell. 1, 155â161 (2019).
Torlai, G. & Melko, R. G. Machine-learning quantum states in the nisq era. Annu. Rev. Condensed Matter Phys. 11, 325â344 (2020).
Torlai, G. et al. Quantum process tomography with unsupervised learning and tensor networks. Nat. Commun. 14, 2858 (2023).
Sweke, R., Kesselring, M. S., Nieuwenburg, E. P. L. & Eisert, J. Reinforcement learning decoders for fault-tolerant quantum computation. Mach. Learn. Sci. Technol. 2, 025005 (2020).
Durrer, R. et al. Automated tuning of double quantum dots into specific charge states using neural networks. Phys. Rev. Appl. 13, 054019 (2020).
Moon, H. et al. Machine learning enables completely automatic tuning of a quantum device faster than human experts. Nat. Commun. 11, 4161 (2020).
Zwolak, J. P. & Taylor, J. M. Advances in automation of quantum dot devices control. Rev. Mod. Phys. 95, 011006 (2023).
Czischek, S. et al. Miniaturizing neural networks for charge state autotuning in quantum dots. Mach. Learn. Sci. Technol. 3, 015001 (2021).
Teoh, Y. H., Drygala, M., Melko, R. G. & Islam, R. Machine learning design of a trapped-ion quantum spin simulator. Quantum Sci. Technol. 5, 024001 (2020).
Carrasquilla, J. Machine learning for quantum matter. Adv. Phys. X 5, 1797528 (2020).
Dawid, A. et al. Modern applications of machine learning in quantum sciences. Preprint at https://arxiv.org/abs/2204.04198 (2022).
Melko, R. G., Carleo, G., Carrasquilla, J. & Cirac, J. I. Restricted Boltzmann machines in quantum physics. Nat. Phys. 15, 887â892 (2019).
Torlai, G. & Melko, R. G. Learning thermodynamics with Boltzmann machines. Phys. Rev. B 94, 165134 (2016).
Torlai, G. et al. Neural-network quantum state tomography. Nat. Phys. 14, 447â450 (2018).
Carleo, G. & Troyer, M. Solving the quantum many-body problem with artificial neural networks. Science 355, 602â606 (2017).
OpenAI: GPT-4 technical report. Preprint at https://arxiv.org/abs/2303.08774 (2023).
Born, M. Quantenmechanik der stoÃvorgänge. Z. Phys. 38, 803â827 (1926).
Wei, V., Coish, W. A., Ronagh, P. & Muschik, C. A. Neural-shadow quantum state tomography. Preprint at https://arxiv.org/abs/2305.01078 (2023).
Islam, R. et al. Measuring entanglement entropy in a quantum many-body system. Nature 528, 77â83 (2015).
Wu, D., Wang, L. & Zhang, P. Solving statistical mechanics using variational autoregressive networks. Phys. Rev. Lett. 122, 080602 (2019).
Liu, J.-G., Mao, L., Zhang, P. & Wang, L. Solving quantum statistical mechanics with variational autoregressive networks and quantum circuits. Mach. Learn. Sci. Technol. 2, 025011 (2021).
Xie, H., Zhang, L. & Wang, L. Ab-initio study of interacting fermions at finite temperature with neural canonical transformation. J. Mach. Learn. 1, 38â59 (2022).
Wang, Z. & Davis, E. J. Calculating Rényi entropies with neural autoregressive quantum states. Phys. Rev. A 102, 062413 (2020).
Sharir, O., Levine, Y., Wies, N., Carleo, G. & Shashua, A. Deep autoregressive models for the efficient variational simulation of many-body quantum systems. Phys. Rev. Lett. 124, 020503 (2020).
Barrett, T. D., Malyshev, A. & Lvovsky, A. I. Autoregressive neural-network wavefunctions for ab initio quantum chemistry. Nat. Mach. Intell. 4, 351â358 (2022).
White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863â2866 (1992).
Orús, R. Tensor networks for complex quantum systems. Nat. Rev. Phys. 1, 538â550 (2019).
Pan, F. & Zhang, P. Simulation of quantum circuits using the big-batch tensor network method. Phys. Rev. Lett. 128, 030501 (2022).
Tindall, J., Fishman, M., Stoudenmire, M. & Sels, D. Efficient tensor network simulation of IBMâs kicked Ising experiment. Preprint at https://arxiv.org/abs/2306.14887 (2023).
Cramer, M. et al. Efficient quantum state tomography. Nat. Commun. 1, 149 (2010).
Cross, A. W., Bishop, L. S., Sheldon, S., Nation, P. D. & Gambetta, J. M. Validating quantum computers using randomized model circuits. Phys. Rev. A 100, 032328 (2019).
Levine, Y., Sharir, O., Cohen, N. & Shashua, A. Quantum entanglement in deep learning architectures. Phys. Rev. Lett. 122, 065301 (2019).
Deng, D.-L., Li, X. & Das Sarma, S. Quantum entanglement in neural network states. Phys. Rev. X 7, 021021 (2017).
Hibat-Allah, M., Ganahl, M., Hayward, L. E., Melko, R. G. & Carrasquilla, J. Recurrent neural network wave functions. Phys. Rev. Res. 2, 023358 (2020).
Roth, C. Iterative retraining of quantum spin models using recurrent neural networks. Preprint at https://arxiv.org/abs/2003.06228 (2020).
Elman, J. L. Finding structure in time. Cogn. Sci. 14, 179â211 (1990).
Hochreiter, S. & Schmidhuber, J. Long short-term memory. Neural Comput. 9, 1735â1780 (1997).
Lipton, Z. C., Berkowitz, J. & Elkan, C. A critical review of recurrent neural networks for sequence learning. Preprint at https://arxiv.org/abs/1506.00019 (2015).
Morawetz, S., De Vlugt, I. J. S., Carrasquilla, J. & Melko, R. G. U(1)-symmetric recurrent neural networks for quantum state reconstruction. Phys. Rev. A 104, 012401 (2021).
Flurin, E., Martin, L. S., Hacohen-Gourgy, S. & Siddiqi, I. Using a recurrent neural network to reconstruct quantum dynamics of a superconducting qubit from physical observations. Phys. Rev. X 10, 011006 (2020).
Hibat-Allah, M., Melko, R. G. & Carrasquilla, J. Supplementing recurrent neural network wave functions with symmetry and annealing to improve accuracy. Preprint at https://arxiv.org/abs/2207.14314 (2022).
Reh, M., Schmitt, M. & Gärttner, M. Optimizing design choices for neural quantum states. Phys. Rev. B 107, 195115 (2023).
Hibat-Allah, M., Melko, R. G. & Carrasquilla, J. Investigating topological order using recurrent neural networks. Phys. Rev. B 108, 075152 (2023).
Luo, D. et al. Gauge-invariant and anyonic-symmetric autoregressive neural network for quantum lattice models. Phys. Rev. Res. 5, 013216 (2023).
Banchi, L., Grant, E., Rocchetto, A. & Severini, S. Modelling non-Markovian quantum processes with recurrent neural networks. New J. Phys. 20, 123030 (2018).
Tang, Y., Weng, J. & Zhang, P. Neural-network solutions to stochastic reaction networks. Nat. Mach. Intell. 5, 376â385 (2023).
Casert, C., Vieijra, T., Whitelam, S. & Tamblyn, I. Dynamical large deviations of two-dimensional kinetically constrained models using a neural-network state ansatz. Phys. Rev. Lett. 127, 120602 (2021).
Reh, M., Schmitt, M. & Gärttner, M. Time-dependent variational principle for open quantum systems with artificial neural networks. Phys. Rev. Lett. 127, 230501 (2021).
Lin, S.-H. & Pollmann, F. Scaling of neural-network quantum states for time evolution. Phys. Status Solidi B 259, 2100172 (2022).
Donatella, K., Denis, Z., Boité, A. L. & Ciuti, C. Dynamics with autoregressive neural quantum states: application to critical quench dynamics. Phys. Rev. A 108, 022210 (2023).
Baireuther, P., OâBrien, T. E., Tarasinski, B. & Beenakker, C. W. J. Machine-learning-assisted correction of correlated qubit errors in a topological code. Quantum 2, 48 (2018).
Chamberland, C. & Ronagh, P. Deep neural decoders for near term fault-tolerant experiments. Quantum Sci. Technol. 3, 044002 (2018).
Baireuther, P., Caio, M. D., Criger, B., Beenakker, C. W. J. & OâBrien, T. E. Neural network decoder for topological color codes with circuit level noise. New J. Phys. 21, 013003 (2019).
Varsamopoulos, S., Bertels, K. & Almudever, C. G. Comparing neural network based decoders for the surface code. IEEE Trans. Comput. 69, 300â311 (2020).
Varbanov, B. M., Serra-Peralta, M., Byfield, D. & Terhal, B. M. Neural network decoder for near-term surface-code experiments. Preprint at https://arxiv.org/abs/2307.03280 (2023).
Czischek, S., Moss, M. S., Radzihovsky, M., Merali, E. & Melko, R. G. Data-enhanced variational Monte Carlo simulations for Rydberg atom arrays. Phys. Rev. B 105, 205108 (2022).
Moss, M. S. et al. Enhancing variational Monte Carlo using a programmable quantum simulator. Preprint at https://arxiv.org/abs/2308.02647 (2023).
Wu, D., Rossi, R., Vicentini, F. & Carleo, G. From tensor-network quantum states to tensorial recurrent neural networks. Phys. Rev. Res. 5, L032001 (2023).
Devlin, J., Chang, M., Lee, K. & Toutanova, K. BERT: pre-training of deep bidirectional transformers for language understanding. In Proc. 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, NAACL-HLT Vol. 1 (eds Burstein, J. et al.) 4171â4186 (Association for Computational Linguistics, 2019).
Taylor, R. et al. Galactica: a large language model for science. Preprint at https://arxiv.org/abs/2211.09085 (2022).
Wei, J. et al. Emergent abilities of large language models. Preprint at https://arxiv.org/abs/2206.07682 (2022).
Vaswani, A. et al. Attention is all you need. In Advances in Neural Information Processing Systems 30 (eds Guyon, Y. et al.) 5998â6008 (NeurIPS, 2017).
Krizhevsky, A., Sutskever, I. & Hinton, G. E. Imagenet classification with deep convolutional neural networks. Commun. ACM 60, 84â90 (2017).
Kaplan, J. et al. Scaling laws for neural language models. Preprint at https://arxiv.org/abs/2001.08361 (2020).
Carrasquilla, J. et al. Probabilistic simulation of quantum circuits using a deep-learning architecture. Phys. Rev. A 104, 032610 (2021).
Cha, P. et al. Attention-based quantum tomography. Mach. Learn. Sci. Technol. 3, 01LT01 (2021).
Wang, H., Weber, M., Izaac, J. & Lin, C.Y.-Y. Predicting properties of quantum systems with conditional generative models. Preprint at https://arxiv.org/abs/2211.16943 (2022).
Ma, H., Sun, Z., Dong, D., Chen, C. & Rabitz, H. Tomography of quantum states from structured measurements via quantum-aware transformer. Preprint at https://arxiv.org/abs/2305.05433 (2023).
Sprague, K. & Czischek, S. Variational Monte Carlo with large patched transformers. Preprint at https://arxiv.org/abs/2306.03921 (2023).
Viteritti, L. L., Rende, R. & Becca, F. Transformer variational wave functions for frustrated quantum spin systems. Phys. Rev. Lett. 130, 236401 (2023).
von Glehn, I., Spencer, J. S. & Pfau, D. A Self-attention ansatz for ab-initio quantum chemistry. Preprint at https://arxiv.org/abs/2211.13672 (2023).
Wu, Y., Guo, C., Fan, Y., Zhou, P. & Shang, H. NNQS-transformer: an efficient and scalable neural network quantum states approach for ab initio quantum chemistry. Preprint at https://arxiv.org/abs/2306.16705 (2023).
Neklyudov, K. et al. Wasserstein quantum Monte Carlo: a novel approach for solving the quantum many-body Schrödinger equation. Preprint at https://arxiv.org/abs/2307.07050 (2023).
Sharir, O., Chan, G. K.-L. & Anandkumar, A. Towards neural variational Monte Carlo that scales linearly with system size. Preprint at https://arxiv.org/abs/2212.11296 (2022).
Zhang, Y.-H. & Di Ventra, M. Transformer quantum state: a multipurpose model for quantum many-body problems. Phys. Rev. B 107, 075147 (2023).
Gao, N. & Günnemann, S. Generalizing neural wave functions. Preprint at https://arxiv.org/abs/2302.04168 (2023).
An, Z., Wu, J., Yang, M., Zhou, D. L. & Zeng, B. Unified quantum state tomography and Hamiltonian learning using transformer models: a language-translation-like approach for quantum systems. Preprint at https://arxiv.org/abs/2304.12010 (2023).
Bennewitz, E. R., Hopfmueller, F., Kulchytskyy, B., Carrasquilla, J. & Ronagh, P. Neural error mitigation of near-term quantum simulations. Nat. Mach. Intell. 4, 618â624 (2022).
Jastrow, R. Many-body problem with strong forces. Phys. Rev. 98, 1479â1484 (1955).
Torlai, G. & Melko, R. G. Neural decoder for topological codes. Phys. Rev. Lett. 119, 030501 (2017).
Cao, H., Pan, F., Wang, Y. & Zhang, P. qecGPT: decoding quantum error-correcting codes with generative pre-trained transformers. Preprint at https://arxiv.org/abs/2307.09025 (2023).
Bausch, J. et al. Learning to decode the surface code with a recurrent, transformer-based neural network. Preprint at https://arxiv.org/abs/2310.05900 (2023).
Chiu, C. S. et al. String patterns in the doped Hubbard model. Science 365, 251â256 (2019).
Becca, F. & Sorella, S. Quantum Monte Carlo Approaches for Correlated Systems (Cambridge Univ. Press, 2017).
Luo, D., Chen, Z., Carrasquilla, J. & Clark, B. K. Autoregressive neural network for simulating open quantum systems via a probabilistic formulation. Phys. Rev. Lett. 128, 090501 (2022).
Gutiérrez, I. L. & Mendl, C. B. Real time evolution with neural-network quantum states. Quantum 6, 627 (2022).
Hibat-Allah, M., Inack, E. M., Wiersema, R., Melko, R. G. & Carrasquilla, J. Variational neural annealing. Nat. Mach. Intell. 3, 952â961 (2021).
Vicentini, F., Rossi, R. & Carleo, G. Positive-definite parametrization of mixed quantum states with deep neural networks. Preprint at https://arxiv.org/abs/2206.13488 (2022).
Acknowledgements
We thank their many students and postdocs who have contributed to these ideas over the years. This work is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Canadian Institute for Advanced Research (CIFAR) AI chair program. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade.
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Melko, R.G., Carrasquilla, J. Language models for quantum simulation. Nat Comput Sci 4, 11â18 (2024). https://doi.org/10.1038/s43588-023-00578-0
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DOI: https://doi.org/10.1038/s43588-023-00578-0