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arXiv · 2506.10191

Constructive interference at the edge of quantum ergodic dynamics

Dmitry A. Abanin·Rajeev Acharya·Laleh Aghababaie-Beni·Georg Aigeldinger·Ashok Ajoy·Ross Alcaraz·Igor Aleiner·Trond I. Andersen·Markus Ansmann·Frank Arute·Kunal Arya·Abraham Asfaw·Nikita Astrakhantsev·Juan Atalaya·Ryan Babbush·Dave Bacon·Brian Ballard·Joseph C. Bardin·Christian Bengs·Andreas Bengtsson·Alexander Bilmes·Sergio Boixo·Gina Bortoli·Alexandre Bourassa·Jenna Bovaird·Dylan Bowers·Leon Brill·Michael Broughton·David A. Browne·Brett Buchea·Bob B. Buckley·David A. Buell·Tim Burger·Brian Burkett·Nicholas Bushnell·Anthony Cabrera·Juan Campero·Hung-Shen Chang·Yu Chen·Zijun Chen·Ben Chiaro·Liang-Ying Chih·Desmond Chik·Charina Chou·Jahan Claes·Agnetta Y. Cleland·Josh Cogan·Saul Cohen·Roberto Collins·Paul Conner·William Courtney·Alexander L. Crook·Ben Curtin·Sayan Das·Laura De Lorenzo·Dripto M. Debroy·Sean Demura·Michel Devoret·Agustin Di Paolo·Paul Donohoe·Ilya Drozdov·Andrew Dunsworth·Clint Earle·Alec Eickbusch·Aviv Moshe Elbag·Mahmoud Elzouka·Catherine Erickson·Lara Faoro·Edward Farhi·Vinicius S. Ferreira·Leslie Flores Burgos·Ebrahim Forati·Austin G. Fowler·Brooks Foxen·Suhas Ganjam·Gonzalo Garcia·Robert Gasca·Elie Genois·William Giang·Craig Gidney·Dar Gilboa·Raja Gosula·Alejandro Grajales Dau·Dietrich Graumann·Alex Greene·Jonathan A. Gross·Hanfeng Gu·Steve Habegger·John Hall·Ikko Hamamura·Michael C. Hamilton·Monica Hansen·Matthew P. Harrigan·Sean D. Harrington·Stephen Heslin·Paula Heu·Oscar Higgott·Gordon Hill·Jeremy Hilton·Sabrina Hong
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Abstract

Quantum observables in the form of few-point correlators are the key to characterizing the dynamics of quantum many-body systems. In dynamics with fast entanglement generation, quantum observables generally become insensitive to the details of the underlying dynamics at long times due to the effects of scrambling. In experimental systems, repeated time-reversal protocols have been successfully implemented to restore sensitivities of quantum observables. Using a 103-qubit superconducting quantum processor, we characterize ergodic dynamics using the second-order out-of-time-order correlators, OTOC$^{(2)}$. In contrast to dynamics without time reversal, OTOC$^{(2)}$ are observed to remain sensitive to the underlying dynamics at long time scales. Furthermore, by inserting Pauli operators during quantum evolution and randomizing the phases of Pauli strings in the Heisenberg picture, we observe substantial changes in OTOC$^{(2)}$ values. This indicates that OTOC$^{(2)}$ is dominated by constructive interference between Pauli strings that form large loops in configuration space. The observed interference mechanism endows OTOC$^{(2)}$ with a high degree of classical simulation complexity, which culminates in a set of large-scale OTOC$^{(2)}$ measurements exceeding the simulation capacity of known classical algorithms. Further supported by an example of Hamiltonian learning through OTOC$^{(2)}$, our results indicate a viable path to practical quantum advantage.

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Dmitry A. Abanin, Rajeev Acharya, Laleh Aghababaie-Beni, Georg Aigeldinger, Ashok Ajoy, Ross Alcaraz, Igor Aleiner, Trond I. Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, Juan Atalaya, Ryan Babbush, Dave Bacon, Brian Ballard, Joseph C. Bardin, Christian Bengs, Andreas Bengtsson, Alexander Bilmes, Sergio Boixo, Gina Bortoli, Alexandre Bourassa, Jenna Bovaird, Dylan Bowers, Leon Brill, Michael Broughton, David A. Browne, Brett Buchea, Bob B. Buckley, David A. Buell, Tim Burger, Brian Burkett, Nicholas Bushnell, Anthony Cabrera, Juan Campero, Hung-Shen Chang, Yu Chen, Zijun Chen, Ben Chiaro, Liang-Ying Chih, Desmond Chik, Charina Chou, Jahan Claes, Agnetta Y. Cleland, Josh Cogan, Saul Cohen, Roberto Collins, Paul Conner, William Courtney, Alexander L. Crook, Ben Curtin, Sayan Das, Laura De Lorenzo, Dripto M. Debroy, Sean Demura, Michel Devoret, Agustin Di Paolo, Paul Donohoe, Ilya Drozdov, Andrew Dunsworth, Clint Earle, Alec Eickbusch, Aviv Moshe Elbag, Mahmoud Elzouka, Catherine Erickson, Lara Faoro, Edward Farhi, Vinicius S. Ferreira, Leslie Flores Burgos, Ebrahim Forati, Austin G. Fowler, Brooks Foxen, Suhas Ganjam, Gonzalo Garcia, Robert Gasca, Elie Genois, William Giang, Craig Gidney, Dar Gilboa, Raja Gosula, Alejandro Grajales Dau, Dietrich Graumann, Alex Greene, Jonathan A. Gross, Hanfeng Gu, Steve Habegger, John Hall, Ikko Hamamura, Michael C. Hamilton, Monica Hansen, Matthew P. Harrigan, Sean D. Harrington, Stephen Heslin, Paula Heu, Oscar Higgott, Gordon Hill, Jeremy Hilton, Sabrina Hong. 2025-06-11. Constructive interference at the edge of quantum ergodic dynamics. https://arxiv.org/abs/2506.10191

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