Quantum computing becomes viable when a quantum state can be protected from environment-induced error. If quantum bits (qubits) are sufficiently reliable, errors are sparse and quantum error correction (QEC)1,2,3,4,5,6 is capable of identifying and correcting them. Adding more qubits improves the preservation of states by guaranteeing that increasingly larger clusters of errors will not cause logical failure—a key requirement for large-scale systems. Using QEC to extend the qubit lifetime remains one of the outstanding experimental challenges in quantum computing. Here we report the protection of classical states from environmental bit-flip errors and demonstrate the suppression of these errors with increasing system size. We use a linear array of nine qubits, which is a natural step towards the two-dimensional surface code QEC scheme7, and track errors as they occur by repeatedly performing projective quantum non-demolition parity measurements. Relative to a single physical qubit, we reduce the failure rate in retrieving an input state by a factor of 2.7 when using five of our nine qubits and by a factor of 8.5 when using all nine qubits after eight cycles. Additionally, we tomographically verify preservation of the non-classical Greenberger–Horne–Zeilinger state. The successful suppression of environment-induced errors will motivate further research into the many challenges associated with building a large-scale superconducting quantum computer.

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  1. 1.

    Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493–R2496 (1995)

  2. 2.

    & Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098–1105 (1996)

  3. 3.

    Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996)

  4. 4.

    & Quantum codes on a lattice with boundary. Preprint at (1998)

  5. 5.

    & Fault-tolerant quantum computation with high threshold in two dimensions. Phys. Rev. Lett. 98, 190504 (2007)

  6. 6.

    , & Topological fault-tolerance in cluster state quantum computation. New J. Phys. 9, 199 (2007)

  7. 7.

    , , & Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012)

  8. 8.

    et al. Experimental quantum error correction. Phys. Rev. Lett. 81, 2152–2155 (1998)

  9. 9.

    , , & Benchmarking quantum computers: the five qubit error correcting code. Phys. Rev. Lett. 86, 5811–5814 (2001)

  10. 10.

    et al. Realization of quantum error correction. Nature 432, 602–605 (2004)

  11. 11.

    et al. Realization of three-qubit quantum error correction with superconducting circuits. Nature 482, 382–385 (2012)

  12. 12.

    et al. Implementing a strand of a scalable fault-tolerant quantum computing fabric. Nature Commun. 5, 4015 (2014)

  13. 13.

    et al. Detecting bit-flip errors in a logical qubit using stabilizer measurements. Preprint at (2014)

  14. 14.

    et al. Quantum computations on a topologically encoded qubit. Science 345, 302–305 (2014)

  15. 15.

    et al. Detecting arbitrary quantum errors via stabilizer measurements on a sublattice of the surface code. Preprint at (2014)

  16. 16.

    et al. Experimental repetitive quantum error correction. Science 332, 1059–1061 (2011)

  17. 17.

    et al. Tracking photon jumps with repeated quantum non-demolition parity measurements. Nature 511, 444–448 (2014)

  18. 18.

    & Quantum measurements and gates by code deformation. J. Phys. A 42, 095302 (2009)

  19. 19.

    et al. Superconducting quantum circuits at the surface code threshold for fault tolerance. Nature 508, 500–503 (2014)

  20. 20.

    et al. Fast accurate state measurement with superconducting qubits. Phys. Rev. Lett. 112, 190504 (2014)

  21. 21.

    et al. Coherent Josephson qubit suitable for scalable quantum integrated circuits. Phys. Rev. Lett. 111, 080502 (2013)

  22. 22.

    , , , & Scalable extraction of error models from the output of error detection circuits. Preprint at (2014)

  23. 23.

    Paths, trees, and flowers. Can. J. Math. 17, 449–467 (1965)

  24. 24.

    Maximum matching and a polyhedron with 0,1-vertices. J. Res. Natl Bur. Stand. B 69, 125–130 (1965)

  25. 25.

    Minimum weight perfect matching of fault-tolerant topological quantum error correction in average O(1) parallel time. Quant. Inform. Comput. 15, 0145–0158 (2015)

  26. 26.

    & Separability criteria for genuine multiparticle entanglement. New J. Phys. 12, 053002 (2010)

  27. 27.

    et al. High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit. Phys. Rev. Lett. 113, 220501 (2014)

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We thank A. N. Korotkov and D. L. Moehring for discussions, and P. Duda for help with photomasks and photolithography. This work was supported by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), through Army Research Office grants W911NF-09-1-0375 and W911NF-10-1-0334. All statements of fact, opinion or conclusions contained herein are those of the authors and should not be construed as representing the official views or policies of IARPA, the ODNI or the US Government. Devices were made at the UC Santa Barbara Nanofabrication Facility, a part of the US NSF-funded National Nanotechnology Infrastructure Network, and at the NanoStructures Cleanroom Facility.

Author information

Author notes

    • J. Kelly
    • , R. Barends
    •  & A. G. Fowler

    These authors contributed equally to this work.

    • R. Barends
    • , A. G. Fowler
    • , E. Jeffrey
    • , D. Sank
    • , J. Y. Mutus
    • , Yu Chen
    • , P. Roushan
    •  & John M. Martinis

    Present address: Google Inc., Santa Barbara, California 93117, USA.


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

    • J. Kelly
    • , R. Barends
    • , A. G. Fowler
    • , A. Megrant
    • , E. Jeffrey
    • , T. C. White
    • , D. Sank
    • , J. Y. Mutus
    • , B. Campbell
    • , Yu Chen
    • , Z. Chen
    • , B. Chiaro
    • , A. Dunsworth
    • , I.-C. Hoi
    • , C. Neill
    • , P. J. J. O’Malley
    • , C. Quintana
    • , P. Roushan
    • , A. Vainsencher
    • , J. Wenner
    • , A. N. Cleland
    •  & John M. Martinis
  2. Centre for Quantum Computation and Communication Technology, School of Physics, The University of Melbourne, Victoria 3010, Australia

    • A. G. Fowler
  3. Department of Materials, University of California, Santa Barbara, California 93106, USA

    • A. Megrant


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J.K. and R.B. designed the sample and performed the experiment. A.G.F. and J.M.M. designed the experiment. J.K., R.B. and A.M. fabricated the sample. A.G.F., J.K. and R.B. analysed the data. J.K., R.B., A.G.F. and J.M.M. co-wrote the manuscript. All authors contributed to the fabrication process, experimental set-up and manuscript preparation.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to J. Kelly or John M. Martinis.

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    Supplementary Information

    This file contains Supplementary Text and Data, Supplementary Figures 1-31, Supplementary Tables 1-3 and additional references.

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