Quantum error correction in a solid-state hybrid spin register

Nature volume 506, pages204–207(2014)Cite this article

Subjects

This article has been updated

Abstract

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.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

Rent or Buy

All prices are NET prices.

Figure 1: Single-shot readout and control of a nuclear spin register via the NV.
Figure 2: Three-qubit entangled states.
Figure 3: Quantum error correction.

Change history

  • 12 February 2014

    A new reference (31) has been added to the main-text reference list and all subsequent references have been renumbered.

References

  1. 1

    Shor, P. W. in Proc. 37th Symp. Foundations Comput. 56–65 (IEEE Comp. Soc. Press, 1996); available at http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=548464

  2. 2

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

    ADS  CAS  Article  Google Scholar 

  3. 3

    Knill, E., Laflamme, R., Martinez, R. & Negrevergne, C. Benchmarking quantum computers: the five-qubit error correcting code. Phys. Rev. Lett. 86, 5811–5814 (2001)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Boulant, N., Viola, L., Fortunato, E. & Cory, D. Experimental implementation of a concatenated quantum error-correcting code. Phys. Rev. Lett. 94, 130501 (2005)

    ADS  Article  Google Scholar 

  5. 5

    Moussa, O., Baugh, J., Ryan, C. A. & Laflamme, R. Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor. Phys. Rev. Lett. 107, 160501 (2011)

    ADS  Article  Google Scholar 

  6. 6

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

    ADS  CAS  Article  Google Scholar 

  7. 7

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

    ADS  CAS  Article  Google Scholar 

  8. 8

    Kane, B. E. A silicon-based nuclear spin quantum computer. Nature 393, 133–137 (1998)

    ADS  CAS  Article  Google Scholar 

  9. 9

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

    ADS  CAS  Article  Google Scholar 

  10. 10

    Neumann, P. et al. Single-shot readout of a single nuclear spin. Science 329, 542–544 (2010)

    ADS  CAS  Article  Google Scholar 

  11. 11

    Koehl, W. F., Buckley, B. B., Heremans, F. J., Calusine, G. & Awschalom, D. D. Room temperature coherent control of defect spin qubits in silicon carbide. Nature 479, 84–87 (2011)

    ADS  CAS  Article  Google Scholar 

  12. 12

    Pla, J. J. et al. A single-atom electron spin qubit in silicon. Nature 489, 541–545 (2012)

    ADS  CAS  Article  Google Scholar 

  13. 13

    Taminiau, T. et al. Detection and control of individual nuclear spins using a weakly coupled electron spin. Phys. Rev. Lett. 109, 137602 (2012)

    ADS  CAS  Article  Google Scholar 

  14. 14

    Pfaff, W. et al. Demonstration of entanglement-by-measurement of solid-state qubits. Nature Phys. 9, 29–33 (2012)

    ADS  Article  Google Scholar 

  15. 15

    Dolde, F. et al. Room-temperature entanglement between single defect spins in diamond. Nature Phys. 9, 139–143 (2013)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Chekhovich, E. A. et al. Nuclear spin effects in semiconductor quantum dots. Nature Mater. 12, 494–504 (2013)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Bernien, H. et al. Heralded entanglement between solid-state qubits separated by three metres. Nature 497, 86–90 (2013)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Maurer, P. C. et al. Room-temperature quantum bit memory exceeding one second. Science 336, 1283–1286 (2012)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Pla, J. J. et al. High-fidelity readout and control of a nuclear spin qubit in silicon. Nature 496, 334–338 (2013)

    ADS  CAS  Article  Google Scholar 

  20. 20

    Yin, C. et al. Optical addressing of an individual erbium ion in silicon. Nature 497, 91–94 (2013)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Kolesov, R. et al. Optical detection of a single rare-earth ion in a crystal. Nature Commun. 3, 1029 (2012)

    ADS  CAS  Article  Google Scholar 

  22. 22

    Le Gall, C., Brunetti, A., Boukari, H. & Besombes, L. Optical Stark effect and dressed exciton states in a Mn-doped CdTe quantum dot. Phys. Rev. Lett. 107, 057401 (2011)

    ADS  CAS  Article  Google Scholar 

  23. 23

    Dutt, M. et al. Quantum register based on individual electronic and nuclear spin qubits in diamond. Science 316, 1312–1316 (2007)

    Article  Google Scholar 

  24. 24

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

    ADS  CAS  Article  Google Scholar 

  25. 25

    Robledo, L. et al. High-fidelity projective read-out of a solid-state spin quantum register. Nature 477, 574–578 (2011)

    ADS  CAS  Article  Google Scholar 

  26. 26

    Taminiau, T. H., Cramer, J., van der Sar, T., Dobrovitski, V. V. & Hanson, R. Universal control and error correction in multi-qubit spin registers in diamond. Preprint at http://arxiv.org/abs/1309.5452 (2013)

  27. 27

    Dréau, A., Spinicelli, P., Maze, J. R., Roch, J.-F. & Jacques, V. Single-shot readout of multiple nuclear spin qubits in diamond under ambient conditions. Phys. Rev. Lett. 110, 060502 (2013)

    ADS  Article  Google Scholar 

  28. 28

    Machnes, S. et al. Comparing, optimizing, and benchmarking quantum-control algorithms in a unifying programming framework. Phys. Rev. A 84, 022305 (2011)

    ADS  Article  Google Scholar 

  29. 29

    Dür, W., Vidal, G. & Cirac, J. I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)

    ADS  MathSciNet  Article  Google Scholar 

  30. 30

    Mermin, N. D. Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65, 1838–1840 (1990)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  31. 31

    Filidou, V. et al. Ultrafast entangling gates between nuclear spins using photo-excited triplet states. Nature Phys. 8, 596–600 (2012)

    ADS  CAS  Article  Google Scholar 

  32. 32

    Mizuochi, N. et al. Coherence of single spins coupled to a nuclear spin bath of varying density. Phys. Rev. B 80, 041201 (2009)

    ADS  Article  Google Scholar 

  33. 33

    Marseglia, L. et al. Nanofabricated solid immersion lenses registered to single emitters in diamond. Appl. Phys. Lett. 98, 133107 (2011)

    ADS  Article  Google Scholar 

  34. 34

    Waldherr, G. et al. Dark states of single nitrogen-vacancy centers in diamond unraveled by single shot NMR. Phys. Rev. Lett. 106, 157601 (2011)

    ADS  CAS  Article  Google Scholar 

  35. 35

    Aslam, N., Waldherr, G., Neumann, P., Jelezko, F. & Wrachtrup, J. Photo-induced ionization dynamics of the nitrogen vacancy defect in diamond investigated by single-shot charge state detection. New J. Phys. 15, 013064 (2013)

    ADS  Article  Google Scholar 

  36. 36

    Waldherr, G. et al. High dynamic range magnetometry with a single nuclear spin in diamond. Nature Nanotechnol. 7, 105–108 (2011)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  37. 37

    Khaneja, N., Reiss, T., Kehlet, C., Schulte-Herbrggen, T. & Glaser, S. J. Optimal control of coupled spin dynamics: design of NMR pulse sequences by gradient ascent algorithms. J. Magn. Reson. 172, 296–305 (2005)

    ADS  CAS  Article  Google Scholar 

  38. 38

    Bell, J. S. On the Einstein Podolsky Rosen paradox. Physics 1, 195–200 (1964)

    MathSciNet  Article  Google Scholar 

  39. 39

    Waldherr, G., Neumann, P., Huelga, S., Jelezko, F. & Wrachtrup, J. Violation of a temporal Bell inequality for single spins in a diamond defect center. Phys. Rev. Lett. 107, 090401 (2011)

    ADS  CAS  Article  Google Scholar 

Download references

Acknowledgements

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

  1. G. Waldherr and Y. Wang: These authors contributed equally to this work.

Affiliations

  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

Authors
  1. G. Waldherr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Y. Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Zaiser
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M. Jamali
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. T. Schulte-Herbrüggen
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. H. Abe
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. T. Ohshima
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. J. Isoya
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. J. F. Du
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. P. Neumann
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. J. Wrachtrup
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

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.

Corresponding author

Correspondence to G. Waldherr.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Extended data figures and tables

Extended Data Figure 1 Hyperfine spectrum as explained in the main text.

Only hyperfine values with an error of less than 4% were used, such that hyperfine values which are close to each other can be resolved.

Extended Data Figure 2 Estimation of number of usable 13C spins.

a, Average number of suitable 13C spins per NV for different 13C concentrations c and different minimum hyperfine (min. h.f.) interactions. Red dots, strongly coupled nuclei; blue triangles, effect of including weakly coupled nuclei with at least 20 kHz hyperfine splitting. b, Spectral density of suitable lattice positions per NV for different magnetic fields B. Note that for these simulations, actual lattice positions are not taken into account. The fluctuations at higher hyperfine interaction are due to numerical grain, that is, due to discretization of the integration volume.

Extended Data Figure 3 Solid immersion lens (SIL).

a, Image of the SIL in diamond. b, Saturation curves of the NV with and without the SIL (measurements were performed with a oil-immersion objective).

Extended Data Figure 4 Full sequence for initialization and readout of the nuclear register.

The ‘main sequence’ part is the actual quantum algorithm, including final local rotations for setting the measurement basis. Note that the charge state post-selection can be substituted by charge state pre-selection34,39.

Extended Data Figure 5 Initialization fidelity of the whole spin register as a function of the number of readout repetitions and the relative shift of the initialization threshold.

The fidelity is colour-coded according to the colour bar.

Extended Data Figure 6 Optimal control.

a, The two microwave frequencies f1 and f2, relative to the electron spin transition frequencies, applied in the experiment. b, The pulse sequence on the left side shows the piecewise-constant control amplitudes (Rabi frequency) for the real and imaginary parts of f1 and f2, where each piece (bar) has a duration of 1.46 µs. It realizes the controlled gate on the electron spin given on the right side.

Extended Data Table 1 Measurement procedure for the Mermin inequality
Full size table
Extended Data Table 2 Measurement procedure and theoretical results for the process fidelity
Full size table

PowerPoint slides

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Waldherr, G., Wang, Y., Zaiser, S. et al. Quantum error correction in a solid-state hybrid spin register. Nature 506, 204–207 (2014). https://doi.org/10.1038/nature12919

Download citation

Further reading

Comments

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.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing