Decoherence-protected quantum gates for a hybrid solid-state spin register

Article metrics



Protecting the dynamics of coupled quantum systems from decoherence by the environment is a key challenge for solid-state quantum information processing1,2. An idle quantum bit (qubit) can be efficiently insulated from the outside world by dynamical decoupling3, as has recently been demonstrated for individual solid-state qubits4,5,6,7,8,9. However, protecting qubit coherence during a multi-qubit gate is a non-trivial problem3,10,11: in general, the decoupling disrupts the interqubit dynamics and hence conflicts with gate operation. This problem is particularly salient for hybrid systems12,13,14,15,16,17,18,19,20,21,22, in which different types of qubit evolve and decohere at very different rates. Here we present the integration of dynamical decoupling into quantum gates for a standard hybrid system, the electron–nuclear spin register. Our design harnesses the internal resonance in the coupled-spin system to resolve the conflict between gate operation and decoupling. We experimentally demonstrate these gates using a two-qubit register in diamond operating at room temperature. Quantum tomography reveals that the qubits involved in the gate operation are protected as accurately as idle qubits. We also perform Grover’s quantum search algorithm1, and achieve fidelities of more than 90% even though the algorithm run-time exceeds the electron spin dephasing time by two orders of magnitude. Our results directly allow decoherence-protected interface gates between different types of solid-state qubit. Ultimately, quantum gates with integrated decoupling may reach the accuracy threshold for fault-tolerant quantum information processing with solid-state devices1,11.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Quantum gate operation in the presence of decoherence.
Figure 2: Decoherence-protected quantum gates for an electron–nuclear spin register.
Figure 3: Performance of the CNOT gate in the presence of strong decoherence.
Figure 4: Grover’s search algorithm executed with decoherence-protected gates.


  1. 1

    Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, 2000)

  2. 2

    Ladd, T. D. et al. Quantum computers. Nature 464, 45–53 (2010)

  3. 3

    Viola, L., Lloyd, S. & Knill, E. Universal control of decoupled quantum systems. Phys. Rev. Lett. 83, 4888–4891 (1999)

  4. 4

    de Lange, G., Wang, Z. H., Ristè, D., Dobrovitski, V. V. & Hanson, R. Universal dynamical decoupling of a single solid-state spin from a spin bath. Science 330, 60–63 (2010)

  5. 5

    Ryan, C. A., Hodges, J. S. & Cory, D. G. Robust decoupling techniques to extend quantum coherence in diamond. Phys. Rev. Lett. 105, 200402 (2010)

  6. 6

    Barthel, C., Medford, J., Marcus, C. M., Hanson, M. P. & Gossard, A. C. Interlaced dynamical decoupling and coherent operation of a singlet-triplet qubit. Phys. Rev. Lett. 105, 266808 (2010)

  7. 7

    Naydenov, B. et al. Dynamical decoupling of a single-electron spin at room temperature. Phys. Rev. B 83, 081201 (2011)

  8. 8

    Bluhm, H. et al. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs. Nature Phys. 7, 109–113 (2011)

  9. 9

    Bylander, J. et al. Noise spectroscopy through dynamical decoupling with a superconducting flux qubit. Nature Phys. 7, 565–570 (2011)

  10. 10

    West, J. R., Lidar, D. A., Fong, B. H. & Gyure, M. F. High fidelity quantum gates via dynamical decoupling. Phys. Rev. Lett. 105, 230503 (2010)

  11. 11

    Ng, K.-H., Lidar, D. A. & Preskill, J. Combining dynamical decoupling with fault-tolerant quantum computation. Phys. Rev. A 84, 012305 (2011)

  12. 12

    Childress, L. et al. Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science 314, 281–285 (2006)

  13. 13

    Childress, L., Taylor, J. M., Sorensen, A. S. & Lukin, M. D. Fault-tolerant quantum communication based on solid-state photon emitters. Phys. Rev. Lett. 96, 070504 (2006)

  14. 14

    Morton, J. J. L. et al. Solid-state quantum memory using the 31P nuclear spin. Nature 455, 1085–1088 (2008)

  15. 15

    Neumann, P. et al. Multipartite entanglement among single spins in diamond. Science 320, 1326–1329 (2008)

  16. 16

    Jiang, L. et al. Repetitive readout of a single electronic spin via quantum logic with nuclear spin ancillae. Science 326, 267–272 (2009)

  17. 17

    Kubo, Y. et al. Strong coupling of a spin ensemble to a superconducting resonator. Phys. Rev. Lett. 105, 140502 (2010)

  18. 18

    Rabl, P. et al. A quantum spin transducer based on nanoelectromechanical resonator arrays. Nature Phys. 6, 602–608 (2010)

  19. 19

    Fuchs, G. D., Burkard, G., Klimov, P. & Awschalom, D. D. A quantum memory intrinsic to single nitrogen–vacancy centres in diamond. Nature Phys. 7, 789–793 (2011)

  20. 20

    Arcizet, O. et al. A single nitrogen-vacancy defect coupled to a nanomechanical oscillator. Nature Phys. 7, 879–883 (2011)

  21. 21

    Cappellaro, P., Viola, L. & Ramanathan, C. Coherent-state transfer via highly mixed quantum spin chain. Phys. Rev. A 83, 032304 (2011)

  22. 22

    Yao, N. Y. et al. Scalable architecture for a room temperature solid-state quantum processor. Nature Commun. (in the press); preprint at 〈〉 (2010)

  23. 23

    Biercuk, M. J. et al. Optimized dynamical decoupling in a model quantum memory. Nature 458, 996–1000 (2009)

  24. 24

    Sagi, Y., Almog, I. & Davidson, N. Process tomography of dynamical decoupling in a dense cold atomic ensemble. Phys. Rev. Lett. 105, 053201 (2010)

  25. 25

    Du, J. et al. Preserving electron spin coherence in solids by optimal dynamical decoupling. Nature 461, 1265–1268 (2009)

  26. 26

    Hanson, R., Dobrovitski, V. V., Feiguin, A. E., Gywat, O. & Awschalom, D. D. Coherent dynamics of a single spin interacting with an adjustable spin bath. Science 320, 352–355 (2008)

  27. 27

    Smeltzer, B., McIntyre, J. & Childress, L. Robust control of individual nuclear spins in diamond. Phys. Rev. A 80, 050302 (2009)

  28. 28

    Steiner, M., Neumann, P., Beck, J., Jelezko, F. & Wrachtrup, J. Universal enhancement of the optical readout fidelity of single electron spins at nitrogen-vacancy centers in diamond. Phys. Rev. B 81, 035205 (2010)

  29. 29

    DiCarlo, L. et al. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009)

  30. 30

    Bermudez, A., Jelezko, F., Plenio, M. B. & Retzker, A. Electron-mediated nuclear-spin interactions between distant NV centers. Phys. Rev. Lett. 107, 150503 (2011)

Download references


We thank L. DiCarlo, F. Jelezko, M. D. Lukin and L. M. K. Vandersypen for discussions and comments. T.v.d.S., H.B. and R.H. acknowledge support from the Dutch Organization for Fundamental Research on Matter and the Netherlands Organization for Scientific Research. D.D.A. acknowledges support from DARPA QuEST, AFOSR and ARO MURI, and R.H. acknowledges support from DARPA QuEST. D.A.L. was sponsored by the National Science Foundation under grant numbers CHM-924318, CHM-1037992 and PHY-0969969, ARO MURI grant W911NF-11-1-0268, and by the US Department of Defense. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressly or implied, of the US Government. Work at Ames Laboratory was supported by the Department of Energy, Basic Energy Sciences under contract number DE-AC02-07CH11358.

Author information

Z.H.W., D.A.L. and V.V.D. designed the gate and did the theoretical analysis. H.B. and D.M.T. made the device. T.v.d.S., M.S.B., T.H.T., D.D.A. and R.H. designed and performed the experiments. T.v.d.S., R.H. and V.V.D. wrote the manuscript. All authors discussed the results and commented on the manuscript.

Correspondence to V. V. Dobrovitski.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Methods and Data, Supplementary Figures 1-13, Supplementary Table 1 and Supplementary References. (PDF 1226 kb)

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

van der Sar, T., Wang, Z., Blok, M. et al. Decoherence-protected quantum gates for a hybrid solid-state spin register. Nature 484, 82–86 (2012) doi:10.1038/nature10900

Download citation

Further reading


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.