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Quantum error correction in a solid-state hybrid spin register

Nature volume 506, pages 204207 (13 February 2014) | Download Citation

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Error correction is important in classical and quantum computation. Decoherence caused by the inevitable interaction of quantum bits with their environment leads to dephasing or even relaxation. Correction of the concomitant errors is therefore a fundamental requirement for scalable quantum computation1,2,3,4,5,6,7. Although algorithms for error correction have been known for some time, experimental realizations are scarce2,3,4,5,6,7. Here we show quantum error correction in a heterogeneous, solid-state spin system8,9,10,11,12,13,14,15,16,17,18,19,20,21. We demonstrate that joint initialization, projective readout and fast local and non-local gate operations can all be achieved in diamond spin systems, even under ambient conditions. High-fidelity initialization of a whole spin register (99 per cent) and single-shot readout of multiple individual nuclear spins are achieved by using the ancillary electron spin of a nitrogen–vacancy defect. Implementation of a novel non-local gate generic to our electron–nuclear quantum register allows the preparation of entangled states of three nuclear spins, with fidelities exceeding 85 per cent. With these techniques, we demonstrate three-qubit phase-flip error correction. Using optimal control, all of the above operations achieve fidelities approaching those needed for fault-tolerant quantum operation, thus paving the way to large-scale quantum computation. Besides their use with diamond spin systems, our techniques can be used to improve scaling of quantum networks relying on phosphorus in silicon19, quantum dots22, silicon carbide11 or rare-earth ions in solids20,21.

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  • 12 February 2014

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We thank F. Dolde, I. Jakobi, M. Kleinmann, F. Jelezko, J. Honert, A. Brunner and C. Walter for experimental help and discussions. We acknowledge financial support from the Max Planck Society, the ERC project SQUTEC, the DFG SFB/TR21, the EU projects DIAMANT, SIQS, QESSENCE and QINVC, the JST-DFG (FOR1482 and FOR1493), and the Volkswagenstiftung.

Author information

Author notes

    • G. Waldherr
    •  & Y. Wang

    These authors contributed equally to this work.


  1. 3. Physikalisches Institut and Research Center SCOPE, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

    • G. Waldherr
    • , Y. Wang
    • , S. Zaiser
    • , M. Jamali
    • , P. Neumann
    •  & J. Wrachtrup
  2. Department of Chemistry, Technical University of Munich, 85747 Garching, Germany

    • T. Schulte-Herbrüggen
  3. Japan Atomic Energy Agency, Takasaki, Gunma 370-1292, Japan

    • H. Abe
    •  & T. Ohshima
  4. Research Center for Knowledge Communities, University of Tsukuba, Tsukuba, Ibaraki 305-8550, Japan

    • J. Isoya
  5. Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China

    • J. F. Du
  6. Max Planck Institute for Solid State Research, Heisenbergstraße 1, 70569 Stuttgart, Germany

    • J. Wrachtrup


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Y.W., G.W., P.N. and J.W. conceived the experiments; G.W. and S.Z. prepared the sample and performed the experiments; Y.W. calculated the robust pulses; Y.W., G.W. and S.Z. analysed the data; J.I., H.A., T.O. and P.N. performed the electron irradiation; M.J. fabricated the SIL; G.W., J.W., P.N., Y.W., T.S.-H. and J.F.D. wrote the manuscript; and P.N. and J.W. supervised the project.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to G. Waldherr.

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