Thermalization and criticality on an analogue–digital quantum simulator

Creators: Andersen, T. I.¹; Astrakhantsev, N.¹; Karamlou, A. H.¹; Berndtsson, J.¹; Motruk, J.²; Szasz, A.¹; Gross, J. A.¹; Schuckert, A.³; Westerhout, T.⁴; Zhang, Y.¹; Forati, E.¹; Rossi, D.²; Kobrin, B.¹; Paolo, A. Di¹; Klots, A. R.¹; Drozdov, I.^{1, 5}; Kurilovich, V.¹; Petukhov, A.¹; Ioffe, L. B.¹; Elben, A.⁶; Rath, A.⁷; Vitale, V.⁷; Vermersch, B.⁷; Acharya, R.¹; Beni, L. A.¹; Anderson, K.¹; Ansmann, M.¹; Arute, F.¹; Arya, K.¹; Asfaw, A.¹; Atalaya, J.¹; Ballard, B.¹; Bardin, J. C.^{1, 8}; Bengtsson, A.¹; Bilmes, A.¹; Bortoli, G.¹; Bourassa, A.¹; Bovaird, J.¹; Brill, L.¹; Broughton, M.¹; Browne, D. A.¹; Buchea, B.¹; Buckley, B. B.¹; Buell, D. A.¹; Burger, T.¹; Burkett, B.¹; Bushnell, N.¹; Cabrera, A.¹; Campero, J.¹; Chang, H.-S.¹; Chen, Z.¹; Chiaro, B.¹; Claes, J.¹; Cleland, A. Y.¹; Cogan, J.¹; Collins, R.¹; Conner, P.¹; Courtney, W.¹; Crook, A. L.¹; Das, S.¹; Debroy, D. M.¹; Lorenzo, L. De¹; Barba, A. Del Toro¹; Demura, S.¹; Donohoe, P.¹; Dunsworth, A.¹; Earle, C.¹; Eickbusch, A.¹; Elbag, A. M.¹; Elzouka, M.¹; Erickson, C.¹; Faoro, L.¹; Fatemi, R.¹; Ferreira, V. S.¹; Burgos, L. Flores¹; Fowler, A. G.¹; Foxen, B.¹; Ganjam, S.¹; Gasca, R.¹; Giang, W.¹; Gidney, C.¹; Gilboa, D.¹; Giustina, M.¹; Gosula, R.¹; Dau, A. Grajales¹; Graumann, D.¹; Greene, A.¹; Habegger, S.¹; Hamilton, M. C.^{1, 9}; Hansen, M.¹; Harrigan, M. P.¹; Harrington, S. D.¹; Heslin, S.^{1, 9}; Heu, P.¹; Hill, G.¹; Hoffmann, M. R.¹; Huang, H.-Y.¹; Huang, T.¹; Huff, A.¹; Huggins, W. J.¹; Isakov, S. V.¹; Jeffrey, E.¹; Jiang, Z.¹; Jones, C.¹; Jordan, S.¹; Joshi, C.¹; Juhas, P.¹; Kafri, D.¹; Kang, H.¹; Kechedzhi, K.¹; Khaire, T.¹; Khattar, T.¹; Khezri, M.¹; Kieferová, M.^{1, 10}; Kim, S.¹; Kitaev, A.¹; Klimov, P.¹; Korotkov, A. N.^{1, 11}; Kostritsa, F.¹; Kreikebaum, J. M.¹; Landhuis, D.¹; Langley, B. W.¹; Laptev, P.¹; Lau, K.-M.¹; Guevel, L. Le¹; Ledford, J.¹; Lee, J.^{1, 12}; Lee, K. W.¹; Lensky, Y. D.¹; Lester, B. J.¹; Li, W. Y.¹; Lill, A. T.¹; Liu, W.¹; Livingston, W. P.¹; Locharla, A.¹; Lundahl, D.¹; Lunt, A.¹; Madhuk, S.¹; Maloney, A.¹; Mandrà, S.¹; Martin, L. S.¹; Martin, O.¹; Martin, S.¹; Maxfield, C.¹; McClean, J. R.¹; McEwen, M.¹; Meeks, S.¹; Miao, K. C.¹; Mieszala, A.¹; Molina, S.¹; Montazeri, S.¹; Morvan, A.¹; Movassagh, R.¹; Neill, C.¹; Nersisyan, A.¹; Newman, M.¹; Nguyen, A.¹; Nguyen, M.¹; Ni, C.-H.¹; Niu, M. Y.¹; Oliver, W. D.¹; Ottosson, K.¹; Pizzuto, A.¹; Potter, R.¹; Pritchard, O.¹; Pryadko, L. P.^{1, 11}; Quintana, C.¹; Reagor, M. J.¹; Rhodes, D. M.¹; Roberts, G.¹; Rocque, C.¹; Rosenberg, E.¹; Rubin, N. C.¹; Saei, N.¹; Sankaragomathi, K.¹; Satzinger, K. J.¹; Schurkus, H. F.¹; Schuster, C.¹; Shearn, M. J.¹; Shorter, A.¹; Shutty, N.¹; Shvarts, V.¹; Sivak, V.¹; Skruzny, J.¹; Small, S.¹; Smith, W. Clarke¹; Springer, S.¹; Sterling, G.¹; Suchard, J.¹; Szalay, M.¹; Sztein, A.¹; Thor, D.¹; Torres, A.¹; Torunbalci, M. M.¹; Vaishnav, A.¹; Vdovichev, S.¹; Villalonga, B.¹; Heidweiller, C. Vollgraff¹; Waltman, S.¹; Wang, S. X.¹; White, T.¹; Wong, K.¹; Woo, B. W. K.¹; Xing, C.¹; Yao, Z. Jamie¹; Yeh, P.¹; Ying, B.¹; Yoo, J.¹; Yosri, N.¹; Young, G.¹; Zalcman, A.¹; Zhu, N.¹; Zobrist, N.¹; Neven, H.¹; Babbush, R.¹; Boixo, S.¹; Hilton, J.¹; Lucero, E.¹; Megrant, A.¹; Kelly, J.¹; Chen, Y.¹; Smelyanskiy, V.¹; Vidal, G.¹; Roushan, P.¹; Läuchli, A. M.^{13, 14}; Abanin, D. A.^{1, 15}; Mi, X.¹

1. Google (United States)
2. University of Geneva
3. Joint Quantum Institute
4. Radboud University Nijmegen
5. University of Connecticut
6. California Institute of Technology
7. Laboratoire de Physique et Modélisation des Milieux Condensés
8. University of Massachusetts Amherst
9. Auburn University
10. University of Technology Sydney
11. University of California, Santa Barbara
12. Harvard University
13. Paul Scherrer Institute
14. École Polytechnique Fédérale de Lausanne
15. Princeton University

Abstract

Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators. Unlocking the full potential of such systems towards this goal requires flexible initial state preparation, precise time evolution and extensive probes for final state characterization. Here we present a quantum simulator comprising 69 superconducting qubits that supports both universal quantum gates and high-fidelity analogue evolution, with performance beyond the reach of classical simulation in cross-entropy benchmarking experiments. This hybrid platform features more versatile measurement capabilities compared with analogue-only simulators, which we leverage here to reveal a coarsening-induced breakdown of Kibble–Zurek scaling predictions in the XY model, as well as signatures of the classical Kosterlitz–Thouless phase transition. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis in targeted parts of the eigenspectrum. We also demonstrate digital preparation of pairwise-entangled dimer states, and image the transport of energy and vorticity during subsequent thermalization in analogue evolution. These results establish the efficacy of superconducting analogue–digital quantum processors for preparing states across many-body spectra and unveiling their thermalization dynamics.

Copyright and License

This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

Acknowledgement

We acknowledge useful discussions with R. Samajdar, D. A. Huse and S. Choi. A. Schuckert acknowledges support from the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator. J.M. acknowledges funding through SNSF Swiss Postdoctoral Fellowship, grant no. 210478. A.E. acknowledges funding by the German National Academy of Sciences Leopoldina under the grant number LPDS 2021-02 and by the Walter Burke Institute for Theoretical Physics at Caltech. Work in Grenoble is funded by the French National Research Agency through the JCJC project QRand (grant no. ANR-20-CE47-0005), Laboratoire d’excellence LANEF (grant no. ANR-10-LABX-51-01), from the Grenoble Nanoscience Foundation.

Data Availability

The data that support the findings in this study are available at Zenodo (https://doi.org/10.5281/zenodo.14060446)

Supplemental Material

Supplementary Information

The Supplementary Information includes Notes 1–13 and Figs. 1–16. In this file, we describe MPS simulations of XY model dynamics, numerical finite-size scaling analysis, alternative correlation fitting schemes and further theoretical analysis of XEB experiments, including computational complexity.

Peer Review File

Files

s41586-024-08460-3.pdf

Files (19.0 MB)

Name	Size	Download all
s41586-024-08460-3.pdf md5:20edb7cdf84b9ae5788ee23247bafd9e	9.1 MB	Preview Download
41586_2024_8460_MOESM1_ESM.pdf md5:1d87cc5ad020d96a03ae69605b8cfc26	9.9 MB	Preview Download

	All versions	This version
Views	0	0
Downloads	0	0
Data volume	0 Bytes	0 Bytes