- Physical Review Journals
All JournalsPhysics Magazine

Physical Review X

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

Quantifying Quantum Computational Advantage on a Processor of Ultracold Atoms

Yong-Guang Zheng1,2,*,∥, Ying-Chao Shen1,2,*, Wei-Yong Zhang1,2,*, An Luo1,2, Ying Liu1,2, Ming-Gen He1,2, Hao-Ran Zhang1,2, Wan Lin1,2, Han-Yi Wang1,2 et al.

Zi-Hang Zhu1,2, Pei-Yue Qiu1,2, Tian-Yi Wang1,2, Ming-Cheng Chen1,2, Chao-Yang Lu1,2,3, Supanut Thanasilp4, Dimitris G. Angelakis4,5,6,7,†, Zhen-Sheng Yuan1,2,3,‡, and Jian-Wei Pan1,2,3,§

  • *These authors contributed equally to this work.
  • †Contact author: d.angelakis@southampton.ac.uk
  • ‡Contact author: yuanzs@ustc.edu.cn
  • §Contact author: pan@ustc.edu.cn
  • ∥Present address: Department of Physics, Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom.
PDF

Phys. Rev. X 16, 021057 – Published 18 June, 2026

DOI: https://doi.org/10.1103/5mqb-3by1

Abstract

Nonequilibrium dynamics of quantum many-body systems is challenging for classical computing, providing opportunities for demonstrating practical quantum computational advantage with analog quantum simulators. Owing to the intimate connection with a random matrix ensemble, it is proposed to be classically intractable to sample the driven thermalized many-body states of a Bose-Hubbard system and further extract multipoint correlations from the output strings for characterizing quantum systems. Here, leveraging dedicated precise manipulations and atom-number-resolved detection through a quantum gas microscope with bichromatic superlattices, we perform sampling of the driven Hubbard chains and two-leg ladders in the thermalized phase involving up to 64 sites with 20 atoms, yielding a Hilbert space dimension of 1019 and outpacing the most powerful supercomputer in terms of sampling rate by 3 orders of magnitude. The volume law scaling of the Rényi entanglement entropy in the thermalized phase is observed, which hinders efficient classical simulation for large systems. We employ the Bayesian tests to verify that our prepared systems operate in the driven thermalized phase. Multipoint correlations of up to 14th-order extracted from the experimental samples offer clear distinctions between the thermalized and many-body-localized phases, where classical computations such as tensor network fail to give accurate and faithful predictions within a reasonable time cost. Our work demonstrates the sampling of an interacting chaotic system performed on a quantum processor of ultracold atoms and opens the door of utilizable quantum computational advantage in simulating Floquet dynamics of many-body systems.

View figure in article

Physics Subject Headings (PhySH)

Popular Summary

Simulating the nonequilibrium dynamics of highly entangled quantum many-body systems presents a formidable challenge for classical computation. To tackle this limitation, we built a quantum processor utilizing ultracold atoms to sample the driven thermalized states of a Bose-Hubbard system that involves up to 64 sites and 20 atoms. We quantitatively verified the output samples from the thermalized phase via Bayesian hypothesis tests and achieved a sampling rate that outperforms the most powerful classical supercomputers by 3 orders of magnitude. Furthermore, we extracted both the entanglement entropy and high-order multipoint correlations to clearly characterize the thermalized phase, a regime where classical tensor network algorithms fail to yield faithful and accurate predictions within a reasonable time. Our observations confirm that specialized analog quantum simulators provide a practical computational advantage for exploring complex dynamics in interacting physical systems.

Article Text

References (88)

  1. J. Zhang et al., Observation of a discrete time crystal, Nature (London) 543, 217 (2017).
  2. S. Choi et al., Observation of discrete time-crystalline order in a disordered dipolar many-body system, Nature (London) 543, 221 (2017).
  3. X. Mi et al., Time-crystalline eigenstate order on a quantum processor, Nature (London) 601, 531 (2022).
  4. A. RubioAbadal, M. Ippoliti, S. Hollerith, D. Wei, J. Rui, S. L. Sondhi, V. Khemani, C. Gross, and I. Bloch, Floquet prethermalization in a Bose-Hubbard system, Phys. Rev. X 10, 021044 (2020).
  5. D. Bluvstein et al., Controlling quantum many-body dynamics in driven Rydberg atom arrays, Science 371, 1355 (2021).
  6. G.-X. Su et al., Observation of many-body scarring in a Bose-Hubbard quantum simulator, Phys. Rev. Res. 5, 023010 (2023).
  7. L. D’Alessio and M. Rigol, Long-time behavior of isolated periodically driven interacting lattice systems, Phys. Rev. X 4, 041048 (2014).
  8. S. Thanasilp, J. Tangpanitanon, M.-A. Lemonde, N. Dangniam, and D. G. Angelakis, Quantum supremacy and quantum phase transitions, Phys. Rev. B 103, 165132 (2021).
  9. A. Lazarides, A. Das, and R. Moessner, Equilibrium states of generic quantum systems subject to periodic driving, Phys. Rev. E 90, 012110 (2014).
  10. P. Ponte, A. Chandran, Z. Papić, and D. A. Abanin, Periodically driven ergodic and many-body localized quantum systems, Ann. Phys. (Amsterdam) 353, 196 (2015).
  11. N. Schuch, M. M. Wolf, F. Verstraete, and J. I. Cirac, Entropy scaling and simulability by matrix product states, Phys. Rev. Lett. 100, 030504 (2008).
  12. A. J. Daley et al., Practical quantum advantage in quantum simulation, Nature (London) 607, 667 (2022).
  13. T. Schweigler et al., Experimental characterization of a quantum many-body system via higher-order correlations, Nature (London) 545, 323 (2017).
  14. R. P. Feynman, Simulating physics with computers, Int. J. Theor. Phys. 21, 467 (1982).
  15. J. Preskill, Quantum computing and the entanglement frontier, Rapporteur Talk at the 25th Solvay Conference on Physics, Brussels (2012), arXiv:1203.5813.
  16. S. Flannigan et al., Propagation of errors and quantitative quantum simulation with quantum advantage, Quantum Sci. Technol. 7, 045025 (2022).
  17. B. M. Terhal, Quantum error correction for quantum memories, Rev. Mod. Phys. 87, 307 (2015).
  18. Y. Kim et al., Evidence for the utility of quantum computing before fault tolerance, Nature (London) 618, 500 (2023).
  19. E. Altman et al., Quantum simulators: Architectures and opportunities, PRX Quantum 2, 017003 (2021).
  20. A. Shaw et al., Benchmarking highly entangled states on a 60-atom analogue quantum simulator, Nature (London) 628, 71 (2024).
  21. A. Young et al., An atomic boson sampler, Nature (London) 629, 311 (2024).
  22. S.-A. Guo et al., A site-resolved two-dimensional quantum simulator with hundreds of trapped ions, Nature (London) 630, 613 (2024).
  23. A. King et al., Beyond-classical computation in quantum simulation, Science 388, 199 (2025).
  24. I. M. Georgescu, S. Ashhab, and F. Nori, Quantum simulation, Rev. Mod. Phys. 86, 153 (2014).
  25. R. Trivedi, A. F. Rubio, and J. I. Cirac, Quantum advantage and stability to errors in analogue quantum simulators, Nat. Commun. 15, 6507 (2024).
  26. J. Tangpanitanon, S. Thanasilp, M.-A. Lemonde, N. Dangiam, and D. G. Angelakis, Signatures of a sampling quantum advantage in driven quantum many-body systems, Quantum Sci. Technol. 8, 025019 (2023).
  27. A. Harrow and A. Montanaro, Quantum computational supremacy, Nature (London) 549, 203 (2017).
  28. F. Arute et al., Quantum supremacy using a programmable superconducting processor, Nature (London) 574, 505 (2019).
  29. Y. Wu et al., Strong quantum computational advantage using a superconducting quantum processor, Phys. Rev. Lett. 127, 180501 (2021).
  30. Q. Zhu et al., Quantum computational advantage via 60-qubit 24-cycle random circuit sampling, Sci. Bull. 67, 240 (2022).
  31. H.-S. Zhong et al., Quantum computational advantage using photons, Science 370, 1460 (2020).
  32. H.-S. Zhong et al., Phase-programmable gaussian boson sampling using stimulated squeezed light, Phys. Rev. Lett. 127, 180502 (2021).
  33. L. S. Madsen et al., Quantum computational advantage with a programmable photonic processor, Nature (London) 606, 75 (2022).
  34. D. Hangleiter and J. Eisert, Computational advantage of quantum random sampling, Rev. Mod. Phys. 95, 035001 (2023).
  35. J. B. Spring et al., Boson sampling on a photonic chip, Science 339, 798 (2013).
  36. M. Tillmann et al., Experimental boson sampling, Nat. Photonics 7, 540 (2013).
  37. A. Crespi et al., Integrated multimode interferometers with arbitrary designs for photonic boson sampling, Nat. Photonics 7, 545 (2013).
  38. J. Carolan et al., On the experimental verification of quantum complexity in linear optics, Nat. Photonics 8, 621 (2014).
  39. H. Wang et al., High-efficiency multiphoton boson sampling, Nat. Photonics 11, 361 (2017).
  40. H. S. Zhong et al., 12-Photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion, Phys. Rev. Lett. 121, 250505 (2018).
  41. M. Bentivegna et al., Bayesian approach to boson sampling validation, Int. J. Quantum. Inform. 12, 1560028 (2014).
  42. M.-D. Li et al., High-powered optical superlattice with robust phase stability for quantum gas microscopy, Opt. Express 29, 13876 (2021).
  43. B. Yang et al., Cooling and entangling ultracold atoms in optical lattices, Science 369, 550 (2020).
  44. W. Y. Zhang et al., Scalable multipartite entanglement created by spin exchange in an optical lattice, Phys. Rev. Lett. 131, 073401 (2023).
  45. Y.-G. Zheng et al., Robust site-resolved addressing via dynamically tracking the phase of optical lattices, Opt. Lett. 47, 4239 (2022).
  46. O. Dutta et al., Non-standard Hubbard models in optical lattices: A review, Rep. Prog. Phys. 78, 066001 (2015).
  47. A. M. Kaufman et al., Quantum thermalization through entanglement in an isolated many-body system, Science 353, 794 (2016).
  48. R. Islam et al., Measuring entanglement entropy in a quantum many-body system, Nature (London) 528, 77 (2015).
  49. T. Brydges et al., Probing Rényi entanglement entropy via randomized measurements, Science 364, 260 (2019).
  50. D. Bluvstein et al., A quantum processor based on coherent transport of entangled atom arrays, Nature (London) 604, 451 (2022).
  51. M. Tajik et al., Verification of the area law of mutual information in a quantum field simulator, Nat. Phys. 19, 1022 (2023).
  52. M. K. Joshi et al., Exploring large-scale entanglement in quantum simulation, Nature (London) 624, 539 (2023).
  53. D. Bluvstein et al., Logical quantum processor based on reconfigurable atom arrays, Nature (London) 626, 58 (2024).
  54. S. S. Hodgman, R. G. Dall, A. G. Manning, K. G. H. Baldwin, and A. G. Truscott, Direct measurement of long-range third-order coherence in Bose-Einstein condensates, Science 331, 1046 (2011).
  55. R. G. Dall et al., Ideal n-body correlations with massive particles, Nat. Phys. 9, 341 (2013).
  56. M. Rispoli et al., Quantum critical behaviour at the many-body localization transition, Nature (London) 573, 385 (2019).
  57. J. Koepsell et al., Microscopic evolution of doped Mott insulators from polaronic metal to Fermi liquid, Science 374, 82 (2021).
  58. M. Magnus, On the exponential solution of differential equa-tions for a linear operator, Commun. Pure Appl. Math. 7, 649 (1954).
  59. X.-K. Wang et al., Low-noise and high-power second harmonic generation of 532 nm laser for trapping ultracold atoms, Rev. Sci. Instrum. 93, 123002 (2022).
  60. S. Blatt, A. Mazurenko, M. F. Parsons, C. S. Chiu, F. Huber, and M. Greiner, Low-noise optical lattices for ultracold Li6, Phys. Rev. A 92, 021402(R) (2015).
  61. S. Stellmer, B. Pasquiou, R. Grimm, and F. Schreck, Laser cooling to quantum degeneracy, Phys. Rev. Lett. 110, 263003 (2013).
  62. J. Hu et al., Creation of a Bose-condensed gas of 87Rb by laser cooling, Science 358, 1078 (2017).
  63. G. A. Phelps et al., Sub-second production of a quantum degenerate gas, arXiv:2007.10807.
  64. H.-Y. Huang et al., Quantum advantage in learning from experiments, Science 376, 1182 (2022).
  65. J. Wang et al., Experimental quantum Hamiltonian learning, Nat. Phys. 13, 551 (2017).
  66. E. Bairey, I. Arad, and N. H. Lindner, Learning a local Hamiltonian from local measurements, Phys. Rev. Lett. 122, 020504 (2019).
  67. Z. Li, L. Zou, and T. H. Hsieh, Hamiltonian tomography via quantum quench, Phys. Rev. Lett. 124, 160502 (2020).
  68. R. Ott, T. V. Zache, M. Prufer, S. Erne, M. Tajik, H. Pichler, J. Schmiedmayer, and P. Zoller, Hamiltonian learning in quantum field theories, Phys. Rev. Res. 6, 043284 (2024).
  69. A. Periwal et al., Programmable interactions and emergent geometry in an array of atom clouds, Nature (London) 600, 630 (2021).
  70. P. Roushan et al., Spectroscopic signatures of localization with interacting photons in superconducting qubits, Science 358, 1175 (2017).
  71. Y.-G. Zheng et al., Quantifying quantum computational advantage on a processor of ultracold atoms (figshare, 2026), 10.6084/m9.figshare.31942533.
  72. B. Xiao et al., Generating two-dimensional quantum gases with high stability, Chin. Phys. B 29, 076701 (2020).
  73. Y.-G. Zheng et al., A compact gain-enhanced microwave helical antenna for 87 Rb atomic experiments, Rev. Sci. Instrum. 93, 064701 (2022).
  74. B. Yang, H. N. Dai, H. Sun, A. Reingruber, Z. S. Yuan, and J. W. Pan, Spin-dependent optical superlattice, Phys. Rev. A 96, 011602 (2017).
  75. M. T. DePue, C. McCormick, S. L. Winoto, S. Oliver, and D. S. Weiss, Unity occupation of sites in a 3D optical lattice, Phys. Rev. Lett. 82, 2262 (1999).
  76. A. J. Daley, H. Pichler, J. Schachenmayer, and P. Zoller, Measuring entanglement growth in quench dynamics of bosons in an optical lattice, Phys. Rev. Lett. 109, 020505 (2012).
  77. A. Lukin et al., Probing entanglement in a many-body–localized system, Science 364, 256 (2019).
  78. S. Stringari, Collective excitations of a trapped Bose-condensed gas, Phys. Rev. Lett. 77, 2360 (1996).
  79. J.-y. Choi et al., Exploring the many-body localization transition in two dimensions, Science 352, 1547 (2016).
  80. P. Weinberg and M. Bukov, Quspin: A python package for dynamics and exact diagonalisation of quantum many body systems. part II: Bosons, fermions and higher spins, SciPost Phys. 7, 020 (2019).
  81. P. Virtanen et al., scipy1.0: Fundamental algorithms for scientific computing in Python, Nat. Methods 17, 261 (2020).
  82. B. Dahlgren, pyodesys: Straightforward numerical integration of ODE systems from Python, J. Open Source Software 3, 490 (2018).
  83. J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, and F. Verstraete, Unifying time evolution and optimization with matrix product states, Phys. Rev. B 94, 165116 (2016).
  84. J. Hauschild and F. Pollmann, Efficient numerical simulations with tensor networks: Tensor network python (tenpy), SciPost Phys. Lect. Notes 5, 005 (2018).
  85. D. K. Mark, J. Choi, A. L. Shaw, M. Endres, and S. Choi, Benchmarking quantum simulators using ergodic quantum dynamics, Phys. Rev. Lett. 131, 110601 (2023).
  86. H. Pishro-Nik, Introduction to Probability, Statistics, and Random Processes (Kappa Research LLC, Boston, 2014).
  87. E. T. Bell, Exponential numbers, Am. Math. Mon. 41, 411 (1934).
  88. H. S. Wilf, Generating Functionology (CRC Press, New York, 2005).

Outline

Information

Phys. Rev. X 16, 021057– Published 18 June, 2026
  • Received 15 December 2024
  • Accepted 3 April 2026
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