Abstract

Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however, the occurrence of ergodic behaviour has remained an outstanding question1,2,3,4. Here, we demonstrate ergodic dynamics in a small quantum system consisting of only three superconducting qubits. The qubits undergo a sequence of rotations and interactions and we measure the evolution of the density matrix. Maps of the entanglement entropy show that the full system can act like a reservoir for individual qubits, increasing their entropy through entanglement. Surprisingly, these maps bear a strong resemblance to the phase space dynamics in the classical limit; classically, chaotic motion coincides with higher entanglement entropy. We further show that in regions of high entropy the full multi-qubit system undergoes ergodic dynamics. Our work illustrates how controllable quantum systems can investigate fundamental questions in non-equilibrium thermodynamics.

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Acknowledgements

We acknowledge discussions with M. Fisher, P. Jessen, V. Madhok, C. Nayak, A. Pattanayak, T. Prosen, A. Rahmani and D. Weld. This work was supported by the NSF under grants DMR-0907039 and DMR-1029764, the AFOSR under FA9550-10-1- 0110, and the ODNI, IARPA, through ARO grant W911NF-10-1-0334. Devices were made at the UCSB Nanofab Facility, part of the NSF-funded NNIN, and the NanoStructures Cleanroom Facility.

Author information

Author notes

    • C. Neill
    • , P. Roushan
    • , M. Fang
    •  & Y. Chen

    These authors contributed equally to this work.

Affiliations

  1. Department of Physics, University of California, Santa Barbara, California 93106-9530, USA

    • C. Neill
    • , M. Fang
    • , Z. Chen
    • , B. Campbell
    • , B. Chiaro
    • , A. Dunsworth
    • , P. J. J. O’Malley
    • , C. Quintana
    • , A. Vainsencher
    • , J. Wenner
    •  & J. M. Martinis
  2. Google Inc., Santa Barbara, California 93117, USA

    • P. Roushan
    • , Y. Chen
    • , A. Megrant
    • , R. Barends
    • , E. Jeffrey
    • , J. Kelly
    • , J. Mutus
    • , D. Sank
    • , T. C. White
    •  & J. M. Martinis
  3. Department of Physics, Boston University, Boston, Massachusetts 02215, USA

    • M. Kolodrubetz
    •  & A. Polkovnikov

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Contributions

C.N., P.R. and Y.C. designed and fabricated the sample and co-wrote the manuscript. C.N., P.R. and M.F. designed the experiment. C.N. performed the experiment and analysed the data. M.K. and A.P. provided theoretical assistance. All members of the UCSB team contributed to the experimental set-up and to the manuscript preparation.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to C. Neill.

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DOI

https://doi.org/10.1038/nphys3830

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