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  • Open Access

Multimodal discrete diffusion for quantum measurement generation in the one-dimensional transverse-field Ising model

YanHong Li and Ho-Kin Tang*

  • School of Science, Harbin Institute of Technology, Shenzhen 518055, China and Shenzhen Key Laboratory of Advanced Functional Carbon Materials Research and Comprehensive Application, Shenzhen 518055, China

  • *Contact author: denghaojian@hit.edu.cn
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APS Open Sci. 1, 000116 – Published 31 August, 2026

DOI: https://doi.org/10.1103/4tft-d7gf

Abstract

Diffusion-based large language models have recently attracted significant interest as a promising class of nonautoregressive generative models. However, their applications to quantum many-body systems remain largely unexplored. We introduce M-Diffushadow, a multimodal diffusion language model for quantum many-body systems. In M-Diffushadow, we adopt a full attention mechanism alongside iterative decoding, which better aligns with the physical characteristics of quantum systems and thereby enables a more faithful modeling of such systems. As a multimodal approach, M-Diffushadow enables bidirectional cross-modal inference, reconstruction from partially observed multimodal records, and fully joint generation without prior measurement outcomes, aligning naturally with realistic experimental constraints where measurement access is limited or incomplete. We demonstrate the effectiveness of the framework on the one-dimensional transverse-field Ising model (TFIM), where generated data accurately reproduce ground-state energies and correlation functions across different phases. We further provide an additional numerical example on the XXZ spin chain to support the applicability of M-Diffushadow beyond the original TFIM benchmark. M-Diffushadow shows the potential to capture and analyze the complex quantum phenomena in quantum many-body systems.

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References (35)

  1. S. Sachdev, Quantum phase transitions, Phys. World 12, 33 (1999).
  2. P. A. Lee, N. Nagaosa, and X.-G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Rev. Mod. Phys. 78, 17 (2006).
  3. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  4. D. Basov, R. Averitt, and D. Hsieh, Towards properties on demand in quantum materials, Nat. Mater. 16, 1077 (2017).
  5. D. Bourgund, T. Chalopin, P. Bojović, H. Schlömer, S. Wang, T. Franz, S. Hirthe, A. Bohrdt, F. Grusdt, I. Bloch, et al., Formation of individual stripes in a mixed-dimensional cold-atom Fermi–Hubbard system, Nature (London) 637, 57 (2025).
  6. A. D. King, A. Nocera, M. M. Rams, J. Dziarmaga, R. Wiersema, W. Bernoudy, J. Raymond, N. Kaushal, N. Heinsdorf, R. Harris, et al., Beyond-classical computation in quantum simulation, Science 388, 199 (2025).
  7. H.-Y. Huang, R. Kueng, and J. Preskill, Predicting many properties of a quantum system from very few measurements, Nat. Phys. 16, 1050 (2020).
  8. G. Struchalin, Y. A. Zagorovskii, E. Kovlakov, S. Straupe, and S. Kulik, Experimental estimation of quantum state properties from classical shadows, PRX Quantum 2, 010307 (2021).
  9. G. Carleo, I. Cirac, K. Cranmer, L. Daudet, M. Schuld, N. Tishby, L. Vogt-Maranto, and L. Zdeborová, Machine learning and the physical sciences, Rev. Mod. Phys. 91, 045002 (2019).
  10. J. Carrasquilla and R. G. Melko, Machine learning phases of matter, Nat. Phys. 13, 431 (2017).
  11. V. Dunjko and H. J. Briegel, Machine learning & artificial intelligence in the quantum domain: A review of recent progress, Rep. Prog. Phys. 81, 074001 (2018).
  12. P. Mehta, M. Bukov, C.-H. Wang, A. G. Day, C. Richardson, C. K. Fisher, and D. J. Schwab, A high-bias, low-variance introduction to machine learning for physicists, Phys. Rep. 810, 1 (2019).
  13. G. Torlai, G. Mazzola, J. Carrasquilla, M. Troyer, R. Melko, and G. Carleo, Neural-network quantum state tomography, Nat. Phys. 14, 447 (2018).
  14. I. J. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio, Generative adversarial nets, in NIPS'14: Proceedings of the 28th International Conference on Neural Information Processing Systems, NIPS'14, Vol. 2 (MIT Press, Cambridge, MA, 2014), pp. 2672–2680.
  15. D. P. Kingma and M. Welling, Auto-encoding variational Bayes, in Proceedings of the 2nd International Conference on Learning Representations (ICLR, Banff, 2014).
  16. A. Radford, J. Wu, R. Child, D. Luan, D. Amodei, and I. Sutskever, Language models are unsupervised multitask learners, OpenAI Blog 1, 9 (2019).
  17. Y. Du, Y. Zhu, Y.-H. Zhang, M.-H. Hsieh, P. Rebentrost, W. Gao, Y.-Z. You, J. Eisert, G. Chiribella, D. Tao, B. C. Sanders, and Y.-D. Wu, Artificial intelligence for representing and characterizing quantum systems, Nat. Rev. Phys. 8, 579 (2026).
  18. S. Nie, F. Zhu, Z. You, X. Zhang, J. Ou, J. Hu, J. Zhou, Y. Lin, J.-R. Wen, and C. Li, Large language diffusion models, Adv. Neural Inf. Process. Syst. 38, 50608 (2025).
  19. F. Zhu, R. Wang, S. Nie, X. Zhang, C. Wu, J. Zhou, Y. Lin, J.-R. Wen, and C. Li, LLaDA 1.5 variance-reduced preference optimization for large language diffusion models, in Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Association for Computational Linguistics, San Diego, 2026), pp. 11425–11460.
  20. J. Ho, A. Jain, and P. Abbeel, Denoising diffusion probabilistic models, in Proceedings of the 34th International Conference on Neural Information Processing Systems (Curran Associates Inc., Red Hook, NY, 2020), pp. 6840–6851.
  21. J. Austin, D. D. Johnson, J. Ho, D. Tarlow, and R. van den Berg, Structured denoising diffusion models in discrete state-spaces, Adv. Neural Inf. Process. Syst. 34, 17981 (2021).
  22. A. Vaswani, N. Shazeer, N. Parmar, J. Uszkoreit, L. Jones, A. N. Gomez, Ł. Kaiser, and I. Polosukhin, Attention is all you need, Adv. Neural Inf. Process. Syst. 30, 5998 (2017).
  23. P. Pfeuty, The one-dimensional Ising model with a transverse field, Ann. Phys. 57, 79 (1970).
  24. B. K. Chakrabarti, A. Dutta, and P. Sen, Quantum Ising Phases and Transitions in Transverse Ising Models (Springer, Berlin, Heidelberg, 1996).
  25. H.-Y. Huang, R. Kueng, and J. Preskill, Efficient estimation of Pauli observables by derandomization, Phys. Rev. Lett. 127, 030503 (2021).
  26. L. Amico, R. Fazio, A. Osterloh, and V. Vedral, Entanglement in many-body systems, Rev. Mod. Phys. 80, 517 (2008).
  27. N. Laflorencie, Quantum entanglement in condensed matter systems, Phys. Rep. 646, 1 (2016).
  28. R. Yu, Q. Li, and X. Wang, Discrete diffusion in large language and multimodal models: A survey, arXiv:2506.13759.
  29. J. Yao and Y.-Z. You, ShadowGPT: Learning to solve quantum many-body problems from randomized measurements, arXiv:2411.03285.
  30. K. Temme, S. Bravyi, and J. M. Gambetta, Error mitigation for short-depth quantum circuits, Phys. Rev. Lett. 119, 180509 (2017).
  31. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020).
  32. S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Semeghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pichler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuletić, and M. D. Lukin, Quantum phases of matter on a 256-atom programmable quantum simulator, Nature (London) 595, 227 (2021).
  33. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357, 995 (2017).
  34. C. Gross and W. S. Bakr, Quantum gas microscopy for single atom and spin detection, Nat. Phys. 17, 1316 (2021).
  35. Y. Li and H.-K. Tang, M-Diffushadow Source code for Multimodal discrete diffusion for quantum measurement generation in the one-dimensional transverse-field Ising model, GitHub repository, 2026, https://github.com/Miamm0v0/M-Diffushadow.

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APS Open Sci. 1, 000116– Published 31 August, 2026
Vol. 1
  • Received 16 February 2026
  • Accepted 17 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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