Observation of constructive interference at the edge of quantum ergodicity
The dynamics of quantum many-body systems is characterized by quantum observables that are reconstructed from correlation functions at separate points in space and time<sup>1-3</sup>. In dynamics with fast entanglement generation, however, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. To circumvent this limitation and enable access to relevant dynamics in experimental systems, repeated time-reversal protocols have been successfully implemented<sup>4</sup>. Here we experimentally measure the second-order out-of-time-order correlators (OTOC<sup>(2)</sup>)<sup>5-18</sup> on a superconducting quantum processor and find that they remain sensitive to the underlying dynamics at long timescales. Furthermore, OTOC<sup>(2)</sup> manifests quantum correlations in a highly entangled quantum many-body system that are inaccessible without time-reversal techniques. This is demonstrated through an experimental protocol that randomizes the phases of Pauli strings in the Heisenberg picture by inserting Pauli operators during quantum evolution. The measured values of OTOC<sup>(2)</sup> are substantially changed by the protocol, thereby revealing constructive interference between Pauli strings that form large loops in the configuration space. The observed interference mechanism also endows OTOC<sup>(2)</sup> with high degrees of classical simulation complexity. These results, combined with the capability of OTOC<sup>(2)</sup> in unravelling useful details of quantum dynamics, as shown through an example of Hamiltonian learning, indicate a viable path to practical quantum advantage.
Authors
- Rebecca Potter (ORCID: https://orcid.org/0000-0002-4671-3423)
- Fionn D. Malone (ORCID: https://orcid.org/0000-0001-9239-0162)
- Leigh S. Martin (ORCID: https://orcid.org/0000-0003-4173-5161)
- Philippe Suchsland (ORCID: https://orcid.org/0000-0001-8936-1539)
- Aaron Shorter
- Hanfeng Gu (ORCID: https://orcid.org/0000-0003-1166-4243)
- Shannon X. Wang
- J. Redding
- Paul Conner
- Vadim Smelyanskiy (ORCID: https://orcid.org/0000-0002-3000-6732)
- Noah Shutty (ORCID: https://orcid.org/0000-0002-6035-2812)
- Eisuke Tomita
- Catherine Vollgraff Heidweiller (ORCID: https://orcid.org/0000-0002-6513-9885)
- Wing Yan Li
- Bicheng Ying (ORCID: https://orcid.org/0000-0002-5246-2982)
- Paula Heu
- Ani Nersisyan (ORCID: https://orcid.org/0000-0001-5450-9943)
- Zlatko Minev (ORCID: https://orcid.org/0000-0003-3759-1847)
- J. Kelly (ORCID: https://orcid.org/0000-0002-2596-2121)
- Jindra Skruzny
- Austin G. Fowler (ORCID: https://orcid.org/0000-0002-9048-2896)
- Leonid P. Pryadko (ORCID: https://orcid.org/0000-0002-4990-0259)
- Rajeev Acharya (ORCID: https://orcid.org/0009-0004-0240-724X)
- Thomas E. O’Brien (ORCID: https://orcid.org/0000-0002-8406-6626)
- Juan Campero
- Kenny Lee (ORCID: https://orcid.org/0000-0001-5396-3626)
- Hartmut Neven (ORCID: https://orcid.org/0000-0002-9681-6746)
- William P. Livingston (ORCID: https://orcid.org/0000-0001-8399-0975)
- Brooks Foxen (ORCID: https://orcid.org/0000-0002-3732-168X)
- Frank Arute (ORCID: https://orcid.org/0000-0002-7179-0631)
- Michael Broughton (ORCID: https://orcid.org/0009-0008-1725-9488)
- Hsin-Yuan Huang (ORCID: https://orcid.org/0000-0001-5317-2613)
- Orion Martin (ORCID: https://orcid.org/0000-0002-9576-573X)
- Alfredo G. Torres (ORCID: https://orcid.org/0000-0001-6450-0643)
- Anthony Cabrera
- Kristoffer Ottosson
- Sean Demura (ORCID: https://orcid.org/0000-0003-3727-7380)
- Ben Curtin (ORCID: https://orcid.org/0000-0002-3856-0615)
- 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)
- Eliott Rosenberg (ORCID: https://orcid.org/0000-0001-5889-8480)
- Jonathan A. Gross (ORCID: https://orcid.org/0000-0001-7049-6206)
- Adam Zalcman (ORCID: https://orcid.org/0000-0002-2585-2424)
- Hui Kang
- Alexander T. Lill (ORCID: https://orcid.org/0000-0001-6692-7931)
- Gina Bortoli (ORCID: https://orcid.org/0009-0008-4597-1691)
- Bob B. Buckley (ORCID: https://orcid.org/0000-0001-5139-7931)
- Brian Lester (ORCID: https://orcid.org/0000-0002-4297-2508)
- D. Sank (ORCID: https://orcid.org/0000-0001-8188-364X)
- Anthony Nguyen (ORCID: https://orcid.org/0000-0002-6215-6954)
- Sayan Das (ORCID: https://orcid.org/0009-0004-4853-1051)
- Ikko Hamamura (ORCID: https://orcid.org/0000-0001-6416-5515)
- Jarrod R. McClean (ORCID: https://orcid.org/0000-0002-2809-0509)
- William J. Huggins (ORCID: https://orcid.org/0000-0003-2735-1380)
- Mostafa Khezri (ORCID: https://orcid.org/0000-0002-3638-6967)
- Erik Lucero (ORCID: https://orcid.org/0000-0002-6449-2273)
- Ofer Naaman (ORCID: https://orcid.org/0000-0002-7760-9186)
- P. Yeh (ORCID: https://orcid.org/0000-0003-0837-1028)
- Alex Opremcak
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- Emma Rosenfeld (ORCID: https://orcid.org/0000-0002-4153-4805)
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- John Mark Kreikebaum (ORCID: https://orcid.org/0000-0002-0253-4183)
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- John A. Hall (ORCID: https://orcid.org/0000-0001-8845-4311)
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- Charles Neill (ORCID: https://orcid.org/0000-0001-8509-9836)
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- 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)
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- Jenna Bovaird (ORCID: https://orcid.org/0000-0002-3331-2786)
- Loïck Le Guevel (ORCID: https://orcid.org/0000-0003-3110-3371)
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- Amir H. Karamlou (ORCID: https://orcid.org/0000-0001-7400-9604)
- Gonzalo Cerruela García (ORCID: https://orcid.org/0000-0001-9140-3347)
- Mustafa Mert Torunbalcı (ORCID: https://orcid.org/0000-0001-9625-669X)
- Ningfeng Zhu (ORCID: https://orcid.org/0000-0002-3037-2003)
- Yossi Matias (ORCID: https://orcid.org/0000-0003-3960-6002)
- Elica Kyoseva (ORCID: https://orcid.org/0000-0002-9154-0293)
- Sergio Boixo (ORCID: https://orcid.org/0000-0002-1090-7584)
- Élie Genois (ORCID: https://orcid.org/0000-0002-2226-1813)
- Dvir Kafri (ORCID: https://orcid.org/0000-0001-9160-5176)
- Fedor Kostritsa
- Brayden Ware (ORCID: https://orcid.org/0000-0002-3321-3198)
- Xiao Mi (ORCID: https://orcid.org/0000-0003-0507-0211)
- Chandrasekhar Ramanathan (ORCID: https://orcid.org/0000-0002-7457-3608)
- Alexandre Bourassa (ORCID: https://orcid.org/0000-0002-8517-7475)
- Oscar Higgott (ORCID: https://orcid.org/0000-0001-9880-5218)
- Aditya Locharla (ORCID: https://orcid.org/0009-0004-5055-9504)
- Ashok Ajoy (ORCID: https://orcid.org/0000-0003-3242-2913)
- Reza Molavi
- Bryce Kobrin
- C. T. Zhang
- Dave Bacon (ORCID: https://orcid.org/0000-0001-6266-9269)
- Sergei V. Isakov
- Alexander L. Crook (ORCID: https://orcid.org/0000-0003-1582-9295)
- Kannan Sankaragomathi (ORCID: https://orcid.org/0000-0001-8930-7081)
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- Negar Saei
- Volodymyr Sivak (ORCID: https://orcid.org/0000-0001-5108-4011)
- L. B. Ioffe (ORCID: https://orcid.org/0000-0002-8777-6789)
- Vladislav D. Kurilovich (ORCID: https://orcid.org/0000-0001-5836-8711)
- Agustín Di Paolo (ORCID: https://orcid.org/0000-0002-5174-7310)
- John Platt (ORCID: https://orcid.org/0000-0002-5652-5303)
- P. Roushan (ORCID: https://orcid.org/0000-0003-1917-3879)
- Paul Donohoe
- Alexis Morvan (ORCID: https://orcid.org/0000-0002-9515-6184)
- Ganesh Ramachandran
- Suhas Ganjam (ORCID: https://orcid.org/0000-0002-3198-3922)
- Pavol Juhás (ORCID: https://orcid.org/0000-0001-8751-4458)
- Joseph C. Bardin (ORCID: https://orcid.org/0000-0002-6523-6730)
- Grayson Young
- M. Neeley (ORCID: https://orcid.org/0000-0002-5548-0051)
- Pavel Laptev
- Bryan W. K. Woo (ORCID: https://orcid.org/0000-0002-7233-1576)
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- Juhwan Yoo
- Gabrielle Roberts (ORCID: https://orcid.org/0000-0003-3309-5205)
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- Josh Cogan
- Amanda Mieszala
- Brian Burkett (ORCID: https://orcid.org/0000-0001-8474-6317)
- Yuri D. Lensky (ORCID: https://orcid.org/0000-0002-8271-516X)
- Jahan Claes (ORCID: https://orcid.org/0000-0002-6711-4585)
- Hung-Shen Chang (ORCID: https://orcid.org/0000-0001-9681-6108)
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- Benjamin Villalonga (ORCID: https://orcid.org/0000-0002-3299-7226)
- Murray Nguyen
- Trond I. Andersen (ORCID: https://orcid.org/0000-0002-7806-1626)
- Alejandro Grajales Dau (ORCID: https://orcid.org/0000-0002-6713-0964)
- Robert Gasca (ORCID: https://orcid.org/0009-0007-8263-091X)
- Trupti Khaire
- Justin Ledford
- Daniel Lundahl
- Sid Madhuk
- Cameron Maxfield
- Orion Pritchard
- Jordan Suchard
- Alex Sztein
- Abeer Vaishnav
- Sergey Vdovichev
- Steven Waltman
- Brett Buchea
- Aviv Moshe Elbag
- Mahmoud Elzouka
- Dietrich Graumann
- Stephen Heslin
- Jiang Zhang (ORCID: https://orcid.org/0000-0003-0435-655X)
- Cheng Xing (ORCID: https://orcid.org/0000-0002-1431-4436)
- Yu Chen (ORCID: https://orcid.org/0000-0002-7473-6745)
- Joon-Ho Lee (ORCID: https://orcid.org/0009-0006-4019-8703)
- Yaxing Zhang (ORCID: https://orcid.org/0000-0002-6940-931X)
- T. White (ORCID: https://orcid.org/0000-0002-9803-7471)
- Zijun Chen (ORCID: https://orcid.org/0000-0001-8642-1604)
- Seon Kim (ORCID: https://orcid.org/0000-0003-3397-0444)
- Andrew Dunsworth
- Christopher Schuster (ORCID: https://orcid.org/0000-0001-5126-3853)
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- Robbie King (ORCID: https://orcid.org/0000-0002-8152-6340)
- Catherine Erickson (ORCID: https://orcid.org/0000-0002-7432-5946)
- A. G. Petukhov
- Spencer Small
- W. Clarke Smith
- Seneca Meeks
- Laleh Aghababaie-Beni
- Tiano Lange-Dei
- Vladimir Shvarts
- Andrey R. Klots
- Lara Faoro
- Steven W. Martin
- Cody Jones
- Guifré Vidal
- Aaron Lunt
- Sofia Springer
- David A. Bowers
- Shannon Leon
- Monica Hansen
- Wayne Liu
- Craig Gidney
- Kevin C. Miao
- Murphy Yuezhen Niu
- Chia-Hung Ni
- Brian Ballard
- David A. Browne
- William Courtney
- E. Jeffrey
- Chris Quintana
- Dripto M. Debroy
- Sebastian Molina
- Kristi Wong
- Clint Earle
- Travis Weidel
- Logan Oas
- Ross Alcaraz
Institutions
- University of California, Riverside (US)
- Dartmouth College (US)
- Canadian Institute for Advanced Research (CA)
- California Institute of Technology (US)
- Ames Research Center (US)
- Google (United States) (US)
- Harvard University (US)
- University of Connecticut (US)
- Lawrence Berkeley National Laboratory (US)
- KBR (United States) (US)
- University of California, Santa Barbara (US)
- Princeton University (US)
- University of Massachusetts Amherst (US)
- Max Planck Institute for the Physics of Complex Systems (DE)
- Nvidia (United States) (US)
- Massachusetts Institute of Technology (US)
- Auburn University (US)
- University of California, Berkeley (US)
Publication Details
- Journal
- Nature
- Published
- 2025-10-22
- DOI
- https://doi.org/10.1038/s41586-025-09526-6
- Citations
- 9
- Primary Topic
- Quantum Computing Algorithms and Architecture
- Type
- article
- Field-Weighted Citation Impact
- 22.33
Funders
- Princeton University
- Curtin University of Technology
- Lawrence Berkeley National Laboratory