Thermalization and criticality on an analogue–digital quantum simulator
Understanding how interacting particles approach thermal equilibrium is a major challenge of quantum simulators<sup>1,2</sup>. 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<sup>3</sup> in the XY model, as well as signatures of the classical Kosterlitz-Thouless phase transition<sup>4</sup>. Moreover, the digital gates enable precise energy control, allowing us to study the effects of the eigenstate thermalization hypothesis<sup>5-7</sup> 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.
Authors
- Luis Lorenzo
- Leigh S. Martin (ORCID: https://orcid.org/0000-0003-4173-5161)
- A. Torres
- B. Ballard (ORCID: https://orcid.org/0000-0003-1206-9358)
- V. S. Ferreira
- Aaron Shorter
- Vadim Smelyanskiy (ORCID: https://orcid.org/0000-0002-3000-6732)
- Noah Shutty (ORCID: https://orcid.org/0000-0002-6035-2812)
- P. Conner
- Rebeca Gasca (ORCID: https://orcid.org/0000-0002-9716-1964)
- Catherine Vollgraff Heidweiller (ORCID: https://orcid.org/0000-0002-6513-9885)
- S. V. Isakov
- Bicheng Ying (ORCID: https://orcid.org/0000-0002-5246-2982)
- A. Dunsworth
- Jeremy Hilton
- Hyunsun Kang (ORCID: https://orcid.org/0000-0002-8451-2059)
- Kam‐Fai Wong (ORCID: https://orcid.org/0000-0002-9427-5659)
- J. Kelly (ORCID: https://orcid.org/0000-0002-2596-2121)
- Jindra Skruzny
- L. B. Ioffe
- Rajeev Acharya (ORCID: https://orcid.org/0009-0004-0240-724X)
- G. Sterling (ORCID: https://orcid.org/0000-0003-4751-3244)
- Juan Campero
- Kenny Lee (ORCID: https://orcid.org/0000-0001-5396-3626)
- Hartmut Neven (ORCID: https://orcid.org/0000-0002-9681-6746)
- F. Kostritsa
- William P. Livingston (ORCID: https://orcid.org/0000-0001-8399-0975)
- Brooks Foxen (ORCID: https://orcid.org/0000-0002-3732-168X)
- Sophie Molina
- R. Potter
- Frank Arute (ORCID: https://orcid.org/0000-0002-7179-0631)
- Michael Broughton (ORCID: https://orcid.org/0009-0008-1725-9488)
- W. Liu (ORCID: https://orcid.org/0009-0005-0503-2209)
- Orion Martin (ORCID: https://orcid.org/0000-0002-9576-573X)
- R. Movassagh
- Kristoffer Ottosson
- Sean Demura (ORCID: https://orcid.org/0000-0003-3727-7380)
- Z. Jamie Yao
- Alex Greene (ORCID: https://orcid.org/0000-0002-4034-8744)
- Nicholas Zobrist (ORCID: https://orcid.org/0000-0003-3146-7263)
- Leslie Flores Burgos
- Dmitry A. Abanin (ORCID: https://orcid.org/0000-0002-2461-0271)
- W. Y. Li
- D. A. Buell
- Steven L. Small (ORCID: https://orcid.org/0000-0002-5293-6172)
- Eliott Rosenberg (ORCID: https://orcid.org/0000-0001-5889-8480)
- Jonathan A. Gross (ORCID: https://orcid.org/0000-0001-7049-6206)
- Hanxia Huang (ORCID: https://orcid.org/0000-0002-1753-7053)
- Adam Zalcman (ORCID: https://orcid.org/0000-0002-2585-2424)
- Alexander T. Lill (ORCID: https://orcid.org/0000-0001-6692-7931)
- Gina Bortoli (ORCID: https://orcid.org/0009-0008-4597-1691)
- Brian Lester (ORCID: https://orcid.org/0000-0002-4297-2508)
- Sabine Springer
- Alexander Schuckert (ORCID: https://orcid.org/0000-0002-9969-7391)
- Sayan Das (ORCID: https://orcid.org/0009-0004-4853-1051)
- Jarrod R. McClean (ORCID: https://orcid.org/0000-0002-2809-0509)
- William J. Huggins (ORCID: https://orcid.org/0000-0003-2735-1380)
- Amiya Kumar Rath (ORCID: https://orcid.org/0000-0002-9956-6973)
- Erik Lucero (ORCID: https://orcid.org/0000-0002-6449-2273)
- Y. Zhang
- M. C. Hamilton
- P. Yeh (ORCID: https://orcid.org/0000-0003-0837-1028)
- C. Xing (ORCID: https://orcid.org/0000-0003-2032-6836)
- Alexei Kitaev (ORCID: https://orcid.org/0000-0002-5777-642X)
- V. Sivak
- Agnetta Y. Cleland (ORCID: https://orcid.org/0000-0002-3932-3881)
- A. G. Fowler
- Aaron Szasz (ORCID: https://orcid.org/0000-0002-1127-2111)
- Alec Eickbusch (ORCID: https://orcid.org/0000-0001-5179-0215)
- L. Brill
- Gordon Hill (ORCID: https://orcid.org/0000-0002-8633-5172)
- Brandon W. Langley
- Ashley Huff
- E. Jeffrey
- R. Collins
- Tom Westerhout (ORCID: https://orcid.org/0000-0003-0200-2686)
- William D. Oliver (ORCID: https://orcid.org/0000-0001-8041-0824)
- A. R. Klots
- William Giang
- C. Quintana
- Steve Habegger (ORCID: https://orcid.org/0000-0001-9867-2371)
- Paula Heu
- Salvatore Mandrà (ORCID: https://orcid.org/0000-0002-3908-2694)
- David Landhuis (ORCID: https://orcid.org/0000-0001-9804-2185)
- Tim Burger
- J. Lee (ORCID: https://orcid.org/0009-0000-6110-2260)
- Douglas Thor (ORCID: https://orcid.org/0009-0001-3013-0100)
- Andreas M. Läuchli (ORCID: https://orcid.org/0000-0002-2272-2691)
- Stephen P. Jordan (ORCID: https://orcid.org/0000-0003-1035-1827)
- Raja Gosula (ORCID: https://orcid.org/0000-0002-3025-7312)
- A. Megrant (ORCID: https://orcid.org/0000-0002-6371-6140)
- Andreas Bengtsson (ORCID: https://orcid.org/0000-0001-5264-4025)
- D. Gilboa
- C. Rocque
- Michael Newman (ORCID: https://orcid.org/0000-0002-6640-1072)
- Reza Fatemi (ORCID: https://orcid.org/0000-0001-9081-2608)
- A. Petukhov
- Nicholas C. Rubin (ORCID: https://orcid.org/0000-0003-3963-1830)
- Ilya Drozdov (ORCID: https://orcid.org/0000-0002-8185-1194)
- A. Nersisyan
- Alexander Del Toro Barba (ORCID: https://orcid.org/0000-0003-0869-5110)
- Mária Kieferová (ORCID: https://orcid.org/0000-0002-0749-8126)
- Henry F. Schurkus (ORCID: https://orcid.org/0000-0002-3210-5929)
- Tanuj Khattar (ORCID: https://orcid.org/0009-0003-5545-3066)
- C. Schuster (ORCID: https://orcid.org/0000-0002-9611-7275)
- B. Chiaro (ORCID: https://orcid.org/0000-0002-2913-2790)
- Nicholas Bushnell (ORCID: https://orcid.org/0000-0001-7445-1654)
- L. P. Pryadko
- Avani S. Vaishnav (ORCID: https://orcid.org/0000-0003-1847-6915)
- A. Pizzuto (ORCID: https://orcid.org/0000-0002-8466-8168)
- S. X. Wang
- John Mark Kreikebaum (ORCID: https://orcid.org/0000-0002-0253-4183)
- Julie G. Ledford (ORCID: https://orcid.org/0000-0001-7977-4575)
- Paul V. Klimov (ORCID: https://orcid.org/0000-0002-9481-4456)
- M. Ansmann (ORCID: https://orcid.org/0000-0001-8765-5621)
- Kevin J. Satzinger (ORCID: https://orcid.org/0000-0001-5865-0813)
- Matthew P. Harrigan (ORCID: https://orcid.org/0000-0001-9412-0553)
- Matt McEwen (ORCID: https://orcid.org/0000-0002-9544-141X)
- Charles Neill (ORCID: https://orcid.org/0000-0001-8509-9836)
- Noureldin Yosri (ORCID: https://orcid.org/0000-0003-4169-5745)
- Abraham Asfaw (ORCID: https://orcid.org/0000-0003-1981-9932)
- Ebrahim Forati (ORCID: https://orcid.org/0000-0002-9917-6246)
- Nikita Astrakhantsev (ORCID: https://orcid.org/0000-0001-6059-1867)
- Ryan Babbush (ORCID: https://orcid.org/0000-0001-6979-9533)
- Matthew J. Reagor (ORCID: https://orcid.org/0000-0003-2576-9097)
- Jenna Bovaird (ORCID: https://orcid.org/0000-0002-3331-2786)
- Loïck Le Guevel (ORCID: https://orcid.org/0000-0003-3110-3371)
- D. M. Debroy
- Amir H. Karamlou (ORCID: https://orcid.org/0000-0001-7400-9604)
- Mustafa Mert Torunbalcı (ORCID: https://orcid.org/0000-0001-9625-669X)
- A. N. Korotkov
- Ningfeng Zhu (ORCID: https://orcid.org/0000-0002-3037-2003)
- Benoît Vermersch (ORCID: https://orcid.org/0000-0001-6781-2079)
- Sergio Boixo (ORCID: https://orcid.org/0000-0002-1090-7584)
- Marco Szalay (ORCID: https://orcid.org/0000-0002-1310-9174)
- Dvir Kafri (ORCID: https://orcid.org/0000-0001-9160-5176)
- Xiao Mi (ORCID: https://orcid.org/0000-0003-0507-0211)
- Alexandre Bourassa (ORCID: https://orcid.org/0000-0002-8517-7475)
- Aditya Locharla (ORCID: https://orcid.org/0009-0004-5055-9504)
- Bryce Kobrin
- A. L. Crook
- Kannan Sankaragomathi (ORCID: https://orcid.org/0000-0001-8930-7081)
- Alexander Bilmes (ORCID: https://orcid.org/0000-0001-5029-915X)
- W. Clarke Smith (ORCID: https://orcid.org/0000-0001-9199-8408)
- Negar Saei
- Vladislav D. Kurilovich (ORCID: https://orcid.org/0000-0001-5836-8711)
- Agustín Di Paolo (ORCID: https://orcid.org/0000-0002-5174-7310)
- M. J. Shearn
- P. Roushan (ORCID: https://orcid.org/0000-0003-1917-3879)
- Johannes Motruk (ORCID: https://orcid.org/0000-0003-4088-8529)
- Y. D. Lensky
- Paul Donohoe
- Alexis Morvan (ORCID: https://orcid.org/0000-0002-9515-6184)
- Suhas Ganjam (ORCID: https://orcid.org/0000-0002-3198-3922)
- M. Hansen
- Pavol Juhás (ORCID: https://orcid.org/0000-0001-8751-4458)
- Joseph C. Bardin (ORCID: https://orcid.org/0000-0002-6523-6730)
- Pavel Laptev
- Bryan W. K. Woo (ORCID: https://orcid.org/0000-0002-7233-1576)
- Andreas Elben (ORCID: https://orcid.org/0000-0003-1444-6356)
- Juan Atalaya (ORCID: https://orcid.org/0000-0003-3055-2730)
- Sanford L. Meeks (ORCID: https://orcid.org/0000-0002-9707-6874)
- Juhwan Yoo
- Kunal Arya (ORCID: https://orcid.org/0000-0002-6486-7100)
- Vittorio Vitale (ORCID: https://orcid.org/0000-0003-4207-9274)
- Kostyantyn Kechedzhi (ORCID: https://orcid.org/0000-0002-0136-1428)
- Kevin C. Miao (ORCID: https://orcid.org/0000-0002-1904-5917)
- M. Giustina
- Brian Burkett (ORCID: https://orcid.org/0000-0001-8474-6317)
- Jahan Claes (ORCID: https://orcid.org/0000-0002-6711-4585)
- Alan Maloney (ORCID: https://orcid.org/0000-0001-8873-1374)
- Hung-Shen Chang (ORCID: https://orcid.org/0000-0001-9681-6108)
- M. R. Hoffmann
- Gareth A. Roberts (ORCID: https://orcid.org/0000-0002-3726-390X)
- S. Kim (ORCID: https://orcid.org/0009-0000-0544-8515)
- Shirin Montazeri (ORCID: https://orcid.org/0000-0002-7124-4585)
- B. Villalonga
- Sean D. Harrington (ORCID: https://orcid.org/0000-0003-0521-8378)
- Kyle R. Anderson (ORCID: https://orcid.org/0000-0001-8041-3996)
- A. Mieszala
- Murray Nguyen
- Trond I. Andersen (ORCID: https://orcid.org/0000-0002-7806-1626)
- Alejandro Grajales Dau (ORCID: https://orcid.org/0000-0002-6713-0964)
- Laleh Aghababaie Beni
- Trupti Khaire
- Daniel Lundahl
- Sid Madhuk
- Cameron Maxfield
- Orion Pritchard
- Jordan Suchard
- Alex Sztein
- Sergey Vdovichev
- Steven Waltman
- Julia Berndtsson
- Brett Buchea
- Aviv Moshe Elbag
- Mahmoud Elzouka
- Dietrich Graumann
- Stephen Heslin
- Jiang Zhang (ORCID: https://orcid.org/0000-0003-0435-655X)
- Yu Chen (ORCID: https://orcid.org/0000-0002-7473-6745)
- T. White (ORCID: https://orcid.org/0000-0002-9803-7471)
- Z. Chen (ORCID: https://orcid.org/0000-0003-1738-3514)
- Chaitanya Joshi (ORCID: https://orcid.org/0000-0002-3886-6585)
- Dario Rossi (ORCID: https://orcid.org/0009-0004-6803-0940)
- David M. Rhodes (ORCID: https://orcid.org/0000-0003-3788-7947)
- Catherine Erickson (ORCID: https://orcid.org/0000-0002-7432-5946)
- D. A. Browne
- Trent Huang (ORCID: https://orcid.org/0009-0000-4650-8115)
- J. Cogan (ORCID: https://orcid.org/0000-0001-7194-7566)
- A. Cabrera
- A. Nguyen
- B. B. Buckley
- Vladimir Shvarts
- Craig Gidney
- Lara Faoro
- Mostafa Khezri
- Steven W. Martin
- Aidan Lunt
- K.-M. Lau
- C. Jones
- Guifré Vidal
- M. Y. Niu (ORCID: https://orcid.org/0000-0002-6528-8522)
- Chia-Hung Ni
- William Courtney
- Clifford J. Earle
- G. Young
Institutions
- University of California, Riverside (US)
- University of Technology Sydney (AU)
- University of Geneva (CH)
- California Institute of Technology (US)
- Google (United States) (US)
- Centre National de la Recherche Scientifique (FR)
- Harvard University (US)
- University of Connecticut (US)
- Radboud University Nijmegen (NL)
- Princeton University (US)
- University of Massachusetts Amherst (US)
- Paul Scherrer Institute (CH)
- Radboud University Medical Center (NL)
- Joint Center for Quantum Information and Computer Science (US)
- Radboud Institute for Molecular Life Sciences (NL)
- Laboratoire de Physique et Modélisation des Milieux Condensés (FR)
- Joint Quantum Institute (US)
- École Polytechnique Fédérale de Lausanne (CH)
- University of Maryland, College Park (US)
- Auburn University (US)
- Université Grenoble Alpes (FR)
Publication Details
- Journal
- Nature
- Published
- 2025-02-05
- DOI
- https://doi.org/10.1038/s41586-024-08460-3
- Citations
- 38
- Primary Topic
- Quantum many-body systems
- Type
- article
- Field-Weighted Citation Impact
- 47.38
Funders
- U.S. Department of Energy
- California Institute of Technology
- Agence Nationale de la Recherche
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung
- Deutsche Akademie der Naturforscher Leopoldina - Nationale Akademie der Wissenschaften
- Office of Science
- Walter Burke Institute for Theoretical Physics