- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Predicting Open Quantum Dynamics with Data-Informed Quantum-Classical Dynamics

Pinchen Xie1,*, Ke Wang2, Anupam Mitra1, Yuanran Zhu1, Xiantao Li2, Wibe Albert de Jong1, and Chao Yang1,†

  • *Contact author: pinchenxie@lbl.gov
  • †Contact author: cyang@lbl.gov
PDF

Phys. Rev. Lett. 136, 010402 – Published 9 January, 2026

DOI: https://doi.org/10.1103/7lsx-ssjl

Abstract

We introduce a data-informed quantum-classical dynamics (DIQCD) approach for predicting the evolution of an open quantum system. The equation of motion in DIQCD is a Lindblad equation with a flexible, time-dependent Hamiltonian that can be optimized to fit sparse and noisy data from local observations of an extensive open quantum system. We demonstrate the accuracy and efficiency of DIQCD for both experimental and simulated quantum devices. We show that DIQCD can predict entanglement dynamics of ultracold molecules (calcium fluoride) in optical tweezer arrays. DIQCD also successfully predicts carrier mobility in organic semiconductors (rubrene) with accuracy comparable to nearly exact numerical methods.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (50)

  1. G. Lindblad, On the generators of quantum dynamical semigroups, Commun. Math. Phys. 48, 119 (1976).
  2. V. Gorini, A. Kossakowski, and E. C. G. Sudarshan, Completely positive dynamical semigroups of n-level systems, J. Math. Phys. (N.Y.) 17, 821 (1976).
  3. A. Garg, J. N. Onuchic, and V. Ambegaokar, Effect of friction on electron transfer in biomolecules, J. Chem. Phys. 83, 4491 (1985).
  4. Y. Tanimura and R. Kubo, Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath, J. Phys. Soc. Jpn. 58, 101 (1989).
  5. B. M. Garraway, Decay of an atom coupled strongly to a reservoir, Phys. Rev. A 55, 4636 (1997).
  6. L. Diósi and W. T. Strunz, The non-Markovian stochastic Schrödinger equation for open systems, Phys. Lett. A 235, 569 (1997).
  7. Y. Tanimura, Stochastic Liouville, Langevin, Fokker–Planck, and master equation approaches to quantum dissipative systems, J. Phys. Soc. Jpn. 75, 082001 (2006).
  8. R.-X. Xu and Y. Yan, Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach, Phys. Rev. E 75, 031107 (2007).
  9. D. Suess, A. Eisfeld, and W. Strunz, Hierarchy of stochastic pure states for open quantum system dynamics, Phys. Rev. Lett. 113, 150403 (2014).
  10. D. Tamascelli, A. Smirne, S. F. Huelga, and M. B. Plenio, Nonperturbative treatment of non-Markovian dynamics of open quantum systems, Phys. Rev. Lett. 120, 030402 (2018).
  11. K. Wang and X. Li, Simulation-assisted learning of open quantum systems, Quantum 8, 1407 (2024).
  12. X. Li, Markovian embedding procedures for non-Markovian stochastic Schrödinger equations, Phys. Lett. A 387, 127036 (2021).
  13. G. Park, Z. Huang, Y. Zhu, C. Yang, G. K.-L. Chan, and L. Lin, Quasi-Lindblad pseudomode theory for open quantum systems, Phys. Rev. B 110, 195148 (2024).
  14. Z. Huang, G. Park, G. K. Chan, and L. Lin, Coupled Lindblad pseudomode theory for simulating open quantum systems, arXiv:2506.10308.
  15. P. Ehrenfest, Bemerkung über die angenäherte gültigkeit der klassischen mechanik innerhalb der quantenmechanik, Z. Phys. 45, 455 (1927).
  16. J. C. Tully, Molecular dynamics with electronic transitions, J. Chem. Phys. 93, 1061 (1990).
  17. J. E. Subotnik, A. Jain, B. Landry, A. Petit, W. Ouyang, and N. Bellonzi, Understanding the surface hopping view of electronic transitions and decoherence, Annu. Rev. Phys. Chem. 67, 387 (2016).
  18. A. L. Shaw, Learning, verifying, and erasing errors on a chaotic and highly entangled programmable quantum simulator, Ph.D. thesis, California Institute of Technology, 2024.
  19. C. M. Holland, Y. Lu, and L. W. Cheuk, On-demand entanglement of molecules in a reconfigurable optical tweezer array, Science 382, 1143 (2023).
  20. W. Li, J. Ren, and Z. Shuai, Finite-temperature TD-DMRG for the carrier mobility of organic semiconductors, J. Phys. Chem. Lett. 11, 4930 (2020).
  21. Y. Cao and J. Lu, Structure-preserving numerical schemes for Lindblad equations, J. Sci. Comput. 102, 27 (2025).
  22. Z. Zhang, X. Liu, K. Yan, M. E. Tuckerman, and J. Liu, Unified efficient thermostat scheme for the canonical ensemble with holonomic or isokinetic constraints via molecular dynamics, J. Phys. Chem. A 123, 6056 (2019).

  23. Such as the damping time in a Langevin process and the angular frequency of an harmonic oscilator.

  24. qepsilon, https://github.com/salinelake/QEpsilon (accessed: 2025-08-26).
  25. A. M. Kaufman and K.-K. Ni, Quantum science with optical tweezer arrays of ultracold atoms and molecules, Nat. Phys. 17, 1324 (2021).
  26. S. Burchesky, L. Anderegg, Y. Bao, S. S. Yu, E. Chae, W. Ketterle, K.-K. Ni, and J. M. Doyle, Rotational coherence times of polar molecules in optical tweezers, Phys. Rev. Lett. 127, 123202 (2021).
  27. Y. Bao, S. S. Yu, L. Anderegg, E. Chae, W. Ketterle, K.-K. Ni, and J. M. Doyle, Dipolar spin-exchange and entanglement between molecules in an optical tweezer array, Science 382, 1138 (2023).

  28. For the experimental molecular temperature [19] without further cooling [29], the quantum fluctuation in r1 and r2 is insignificant.

  29. Y. Lu, S. J. Li, C. M. Holland, and L. W. Cheuk, Raman sideband cooling of molecules in an optical tweezer array, Nat. Phys. 20, 389 (2024).

  30. The word “flexible” indicates quantities that will be optimized with data.

  31. L. Viola, E. Knill, and S. Lloyd, Dynamical decoupling of open quantum systems, Phys. Rev. Lett. 82, 2417 (1999).

  32. K^0=1−pI^, K^1=(p/3)σ^x, K^2=(p/3)σ^y, and K^3=(p/3)σ^z.

  33. See Supplemental Code in [24] for the evolution of all parameters during the training.

  34. The qubit loss is severe for d<1.68  μm due to parametric heating of molecules. For the same reason, the current DIQCD model with a fixed molecular temperature cannot be directly applied to d<1.68  μm.

  35. H. M. Wiseman and G. J. Milburn, Quantum theory of optical feedback via homodyne detection, Phys. Rev. Lett. 70, 548 (1993).
  36. D. Marx and M. Parrinello, Ab initio path integral molecular dynamics: Basic ideas, J. Chem. Phys. 104, 4077 (1996).
  37. J. Mei, Y. Diao, A. L. Appleton, L. Fang, and Z. Bao, Integrated materials design of organic semiconductors for field-effect transistors, J. Am. Chem. Soc. 135, 6724 (2013).
  38. J. Takeya, M. Yamagishi, Y. Tominari, R. Hirahara, Y. Nakazawa, T. Nishikawa, T. Kawase, T. Shimoda, and S. Ogawa, Very high-mobility organic single-crystal transistors with in-crystal conduction channels, Appl. Phys. Lett. 90, 102120 (2007).
  39. X. Ren, M. J. Bruzek, D. A. Hanifi, A. Schulzetenberg, Y. Wu, C.-H. Kim, Z. Zhang, J. E. Johns, A. Salleo, S. Fratini et al., Negative isotope effect on field-effect hole transport in fully substituted 13c-rubrene, Adv. Electron. Mater. 3, 1700018 (2017).

  40. This happens to be the case for most high-mobility organic semiconductors.

  41. The success of TD-DMRG is also limited to 1D due to the 1D nature of the matrix product state and the numerical inefficiency of higher-dimensional tensor networks.

  42. Y. Jiang, X. Zhong, W. Shi, Q. Peng, H. Geng, Y. Zhao, and Z. Shuai, Nuclear quantum tunnelling and carrier delocalization effects to bridge the gap between hopping and bandlike behaviors in organic semiconductors, Nanoscale Horiz. 1, 53 (2016).
  43. A. D. Becke, Density-functional thermochemistry. III. The role of exact exchange, J. Chem. Phys. 98, 5648 (1993).
  44. C. Lee, W. Yang, and R. G. Parr, Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density, Phys. Rev. B 37, 785 (1988).
  45. M. J. Frisch et al., gaussian 09 Revision D.01 ed. (Gaussian Inc., Wallingford, CT, 2009).

  46. Results are not sensitive to the choice of ϕ.

  47. L. Wang, D. Beljonne, L. Chen, and Q. Shi, Mixed quantum-classical simulations of charge transport in organic materials: Numerical benchmark of the Su-Schrieffer-Heeger model, J. Chem. Phys. 134, 244116 (2011).
  48. H.-D. Meyer, U. Manthe, and L. S. Cederbaum, The multi-configurational time-dependent Hartree approach, Chem. Phys. Lett. 165, 73 (1990).
  49. Documentation of qepsilon, https://qepsilon.readthedocs.io/en/latest/ (accessed: 2025-08-26).
  50. R. Kubo, The fluctuation-dissipation theorem, Rep. Prog. Phys. 29, 255 (1966).

Outline

Information

Phys. Rev. Lett. 136, 010402– Published 9 January, 2026
  • Received 28 August 2025
  • Revised 8 November 2025
  • Accepted 19 December 2025
Crossmark - Check for updates button
Creative Commons Logo

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.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation