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Probing quantum information propagation with out-of-time-ordered correlators

Nature Physics volume 18, pages 172–178 (2022)Cite this article

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Abstract

Interacting many-body quantum systems show a rich array of physical phenomena and dynamical properties, but are notoriously difficult to study: they are analytically challenging and exponentially hard to simulate on classical computers. Small-scale quantum information processors hold the promise to efficiently emulate these systems, but characterizing their dynamics is experimentally difficult, requiring probes beyond simple correlation functions and multi-body tomographic methods. Here we demonstrate the measurement of out-of-time-ordered correlators—one of the most effective tools for studying quantum system evolution and processes like quantum thermalization. We implement a 3 × 3 two-dimensional hard-core Bose–Hubbard lattice with a superconducting circuit, study its time reversibility by performing a Loschmidt echo, and measure out-of-time-ordered correlators that enable us to observe the propagation of quantum information. A central requirement for our experiments is the ability to coherently reverse time evolution, which was achieved with a digital–analogue simulation scheme. In the presence of frequency disorder, we observe that localization can partially be overcome with more particles present—a possible signature of many-body localization in two dimensions.

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Fig. 1: Experimental concept.
Fig. 2: Loschmidt echo in the degenerate lattice.
Fig. 3: Quantum random walk and information propagation via OTOC measurements.
Fig. 4: OTOC measurements in disordered lattices.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The code used for numerical simulations and data analyses is available from the corresponding author upon reasonable request.

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Acknowledgements

We are grateful to P. M. Harrington, A. D. Paolo, S. Muschinske and B. Swingle for insightful discussions, and M. Pulido and C. Watanabe for administrative assistance. M.K. acknowledges support from the Carlsberg Foundation during part of this work. A.H.K. acknowledges support from the NSF Graduate Research Fellowships Program. This research was funded in part by the US Army Research Office Grant W911NF-18-1-0411 and the Assistant Secretary of Defense for Research & Engineering under Air Force contract no. FA8721-05-C-0002. Opinions, interpretations, conclusions and recommendations are those of the authors and are not necessarily endorsed by the US government.

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Authors and Affiliations

  1. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Jochen Braumüller, Amir H. Karamlou, Bharath Kannan, Morten Kjaergaard, Youngkyu Sung, Antti Vepsäläinen, Roni Winik, Terry P. Orlando, Simon Gustavsson & William D. Oliver

  2. Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA

    Amir H. Karamlou, Bharath Kannan, Youngkyu Sung, Terry P. Orlando & William D. Oliver

  3. Laboratory for Physical Sciences, College Park, MD, USA

    Yariv Yanay & Charles Tahan

  4. MIT Lincoln Laboratory, Lexington, MA, USA

    David Kim, Alexander Melville, Bethany M. Niedzielski, Jonilyn L. Yoder & William D. Oliver

  5. Department of Physics, Massachusetts Institute of Technology, Cambridge, MA, USA

    William D. Oliver

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  1. Jochen Braumüller
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Contributions

J.B., A.H.K., Y.Y., C.T. and W.D.O. conceived the experiment. Y.Y. developed the pulse sequences for rewinding time and extracting OTOCs and generated the numerical simulations of the OTOCs. J.B. and A.H.K. performed the experiments with theoretical support from Y.Y. J.B., A.H.K., B.K., M.K., Y.S., A.V., R.W. and S.G. developed the experiment control tools used in this work. D.K., A.M., B.N. and J.Y. fabricated the 3 × 3 qubit array. T.P.O., S.G., C.T. and W.D.O. provided experimental oversight and support. All the authors contributed to the discussions of the results and to the development of the manuscript.

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Correspondence to Jochen Braumüller.

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Peer review information Nature Physics thanks Arghavan Safavi-Naini, Lea Santos and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Information

Supplementary Sections 1–10, Figs. 1–12 and Tables 1 and 2.

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Braumüller, J., Karamlou, A.H., Yanay, Y. et al. Probing quantum information propagation with out-of-time-ordered correlators. Nat. Phys. 18, 172–178 (2022). https://doi.org/10.1038/s41567-021-01430-w

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