Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

A silicon quantum-dot-coupled nuclear spin qubit

Nature Nanotechnology volume 15, pages 13–17 (2020)Cite this article

Subjects

Abstract

Single nuclear spins in the solid state are a potential future platform for quantum computing1,2,3, because they possess long coherence times4,5,6 and offer excellent controllability7. Measurements can be performed via localized electrons, such as those in single atom dopants8,9 or crystal defects10,11,12. However, establishing long-range interactions between multiple dopants or defects is challenging13,14. Conversely, in lithographically defined quantum dots, tunable interdot electron tunnelling allows direct coupling of electron spin-based qubits in neighbouring dots15,16,17,18,19,20. Moreover, the compatibility with semiconductor fabrication techniques21 may allow for scaling to large numbers of qubits in the future. Unfortunately, hyperfine interactions are typically too weak to address single nuclei. Here we show that for electrons in silicon metal–oxide–semiconductor quantum dots the hyperfine interaction is sufficient to initialize, read out and control single 29Si nuclear spins. This approach combines the long coherence times of nuclear spins with the flexibility and scalability of quantum dot systems. We demonstrate high-fidelity projective readout and control of the nuclear spin qubit, as well as entanglement between the nuclear and electron spins. Crucially, we find that both the nuclear spin and electron spin retain their coherence while moving the electron between quantum dots. Hence we envision long-range nuclear–nuclear entanglement via electron shuttling3. Our results establish nuclear spins in quantum dots as a powerful new resource for quantum processing.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Hyperfine coupling in a silicon metal–oxide quantum dot.
Fig. 2: 29Si nuclear spin qubit control and readout.
Fig. 3: Entanglement between nuclear and electron spin states.
Fig. 4: Nuclear and electron spin coherence during electron transfer.

Similar content being viewed by others

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

References

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

    Article  CAS  Google Scholar 

  2. Ladd, T. D. et al. All-silicon quantum computer. Phys. Rev. Lett. 89, 017901 (2002).

    Article  CAS  Google Scholar 

  3. Skinner, A. J., Davenport, M. E. & Kane, B. E. Hydrogenic spin quantum computing in silicon: a digital approach. Phys. Rev. Lett. 90, 087901 (2003).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  5. Saeedi, K. et al. Room-temperature quantum bit storage exceeding 39 minutes using ionized donors in silicon-28. Science 342, 830–833 (2013).

    Article  CAS  Google Scholar 

  6. Muhonen, J. T. et al. Storing quantum information for 30 seconds in a nanoelectronic device. Nat. Nanotechnol. 9, 986–991 (2014).

    Article  CAS  Google Scholar 

  7. Vandersypen, L. M. K. & Chuang, I. L. NMR techniques for quantum control and computation. Rev. Mod. Phys. 76, 1037–1069 (2005).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

  9. Pla, J. J. et al. Coherent control of a single 29Si nuclear spin qubit. Phys. Rev. Lett. 113, 246801 (2014).

    Article  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  12. Abobeih, M. H. et al. One-second coherence for a single electron spin coupled to a multi-qubit nuclear-spin environment. Nat. Commun. 9, 2552 (2018).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  14. Tosi, G. et al. Silicon quantum processor with robust long-distance qubit couplings. Nat. Commun. 8, 450 (2017).

    Article  Google Scholar 

  15. Nowack, K. C. et al. Single-shot correlations and two-qubit gate of solid-state spins. Science 333, 1269–1272 (2011).

    Article  CAS  Google Scholar 

  16. Veldhorst, M. et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nat. Nanotechnol. 9, 981–985 (2014).

    Article  CAS  Google Scholar 

  17. Veldhorst, M. et al. A two-qubit logic gate in silicon. Nature 526, 410–414 (2015).

    Article  CAS  Google Scholar 

  18. Watson, T. F. et al. A programmable two-qubit quantum processor in silicon. Nature 555, 633–637 (2018).

    Article  CAS  Google Scholar 

  19. Zajac, D. M. et al. Resonantly driven CNOT gate for electron spins. Science 359, 439–442 (2018).

    Article  CAS  Google Scholar 

  20. Huang, W. et al. Fidelity benchmarks for two-qubit gates in silicon. Nature 569, 532–536 (2019).

    Article  CAS  Google Scholar 

  21. Maurand, R. et al. A CMOS silicon spin qubit. Nat. Commun. 7, 13575 (2016).

    Article  CAS  Google Scholar 

  22. Johnson, A. C. et al. Triplet–singlet spin relaxation via nuclei in a double quantum dot. Nature 435, 925–928 (2005).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  24. Yang, C. H. et al. Spin-valley lifetimes in a silicon quantum dot with tunable valley splitting. Nat. Commun. 4, 2069 (2013).

    Article  CAS  Google Scholar 

  25. Assali, L. V. C. et al. Hyperfine interactions in silicon quantum dots. Phys. Rev. B 83, 165301 (2011).

    Article  Google Scholar 

  26. Elzerman, J. M. et al. Single-shot read-out of an individual electron spin in a quantum dot. Nature 430, 431–435 (2004).

    Article  CAS  Google Scholar 

  27. Dehollain, J. P. et al. Bell’s inequality violation with spins in silicon. Nat. Nanotechnol. 11, 242–246 (2016).

    Article  CAS  Google Scholar 

  28. Wolfowicz, G. et al. 29Si nuclear spins as a resource for donor spin qubits in silicon. New J. Phys. 18, 023021 (2016).

    Article  Google Scholar 

  29. Pica, G., Lovett, B. W., Bhatt, R. N., Schenkel, T. & Lyon, S. A. Surface code architecture for donors and dots in silicon with imprecise and nonuniform qubit couplings. Phys. Rev. B 93, 035306 (2016).

    Article  Google Scholar 

  30. Harvey-Collard, P. et al. Coherent coupling between a quantum dot and a donor in silicon. Nat. Commun. 8, 1029 (2017).

    Article  Google Scholar 

  31. Fujita, T., Baart, T. A., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Coherent shuttle of electron-spin states. Npj Quantum Inf. 3, 22 (2017).

    Article  Google Scholar 

  32. Freer, S. et al. A single-atom quantum memory in silicon. Quantum Sci. Technol. 2, 015009 (2017).

    Article  Google Scholar 

  33. Mi, X. et al. A coherent spin–photon interface in silicon. Nature 555, 599–603 (2018).

    Article  CAS  Google Scholar 

  34. Samkharadze, N. et al. Strong spin–photon coupling in silicon. Science 359, 1123–1127 (2018).

    Article  CAS  Google Scholar 

  35. Bennett, C. H. et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996).

    Article  CAS  Google Scholar 

  36. Nickerson, N. H., Li, Y. & Benjamin, S. C. Topological quantum computing with a very noisy network and local error rates approaching one percent. Nat. Commun. 4, 1756 (2013).

    Article  Google Scholar 

  37. Mazzocchi, V. et al. 99.992% 28Si CVD-grown epilayer on 300 mm substrates for large scale integration of silicon spin qubits. J. Cryst. Growth 509, 1–7 (2019).

    Article  CAS  Google Scholar 

  38. Donkelaar, J. Van et al. Single atom devices by ion implantation. J. Phys. Condens. Matter 27, 154204 (2015).

    Article  Google Scholar 

  39. Davies, J. H. The Physics of Low-dimensional Semiconductors: An Introduction (Cambridge Univ. Press, 1997).

Download references

Acknowledgements

We thank C. Escott, P. Harvey-Collard, V. V. Dobrovitski for valuable discussions and feedback on the manuscript, and J. J. Pla for technical assistance. We acknowledge support from the US Army Research Office (W911NF-17-1-0198), the Australian Research Council (CE170100012), Silicon Quantum Computing Proprietary Limited and the NSW Node of the Australian National Fabrication Facility. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the Army Research Office or the US Government. B.H. acknowledges support from the Netherlands Organisation for Scientific Research (NWO) through a Rubicon Grant. K.M.I. acknowledges support from a Grant-in-Aid for Scientific Research by MEXT.

Author information

Author notes

  1. Bas Hensen

    Present address: Delft University of Technology, Delft, The Netherlands

  2. These authors contributed equally: Bas Hensen, Wister Wei Huang.

Authors and Affiliations

  1. Center for Quantum Computation and Communication Technology, School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney, New South Wales, Australia

    Bas Hensen, Wister Wei Huang, Chih-Hwan Yang, Kok Wai Chan, Jun Yoneda, Tuomo Tanttu, Fay E. Hudson, Arne Laucht, Andrea Morello & Andrew S. Dzurak

  2. School of Fundamental Science and Technology, Keio University, Yokohama, Japan

    Kohei M. Itoh

  3. HRL Laboratories, Malibu, CA, USA

    Thaddeus D. Ladd

Authors
  1. Bas Hensen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wister Wei Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chih-Hwan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kok Wai Chan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jun Yoneda
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Tuomo Tanttu
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Fay E. Hudson
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Arne Laucht
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Kohei M. Itoh
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Thaddeus D. Ladd
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Andrea Morello
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Andrew S. Dzurak
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

B.H. and W.W.H. performed the experiments. K.W.C. and F.E.H. fabricated the devices. K.M.I. prepared and supplied the 28Si wafer. B.H., W.W.H., C.-H.Y., J.Y., T.T. and A.L. designed the experiments. B.H., W.W.H. and J.Y. analysed the data. T.D.L. performed hyperfine and coherence simulations. B.H. wrote the manuscript with input from all co-authors. A.M., A.L. and A.S.D. supervised the project.

Corresponding author

Correspondence to Andrew S. Dzurak.

Ethics declarations

Competing interests

This work was funded, in part, by Silicon Quantum Computing Proprietary Limited.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 Expected hyperfine interaction.

a, Maximum possible hyperfine interaction for given dot diameter, defined as the 1/e point of the envelope charge distribution, and vertical confining electric field Fz. b, Probability of observing at least one nuclear spin with hyperfine coupling |A| ≥ 100 kHz (dashed line), |A| ≥ 200 kHz (solid line) and |A| ≥ 500 kHz (dotted line), for 800 ppm 29Si material. These distributions are found by calculating the electron wavefunction density for an Airy envelope function39, sinusoidally oscillating in the vertical dimension due to valley oscillations, and with a transverse Gaussian shape, all superimposed over an unstrained silicon lattice. We assume 29Si are randomly placed with 800 ppm probability at each lattice site and evaluate the resulting hyperfine contact interaction25. The probabilities grow with dot diameter due to increased number of sites overlapped, but then shrink for large dots due the reducing hyperfine contact at each site.

Source data

Extended Data Fig. 2 Ramsey and Hahn echo measurement in the (0,0) charge state.

a, Ramsey measurement and b, Hahn echo measurement with nuclear pulses and free evolution time in charge configuration (0,0). Resulting values T2*,(0,0) = 6.0 ± 0.6 ms and T2Hahn,(0,0) = 13.1 ± 1.5 ms are within error to those obtained for the unloaded-(0,1) charge configuration, see Fig. 2g, i.

Source data

Extended Data Fig. 3 Second 29Si qubit coupled to quantum dot QD2.

a, NMR frequency scan with QD2 loaded with a spin-↓ electron, charge configuration (0,1), reveals a 29Si nuclear spin coupled by AQD2 = −179.8 ± 0.2 kHz. Note that the nuclear spin readout contrast is reduced due to the small hyperfine splitting. b, Loaded Ramsey measurement yields T2*,loaded = 21 ± 5 ms, for 1 hour integration time. c, Loaded Hahn echo measurement yields T2Hahn, loaded = 42 ± 11 ms. d, Unloaded, charge state (0,0), Hahn echo yields T2Hahn,(0,0) = 40 ± 13 ms.

Source data

Extended Data Fig. 4 Nuclear-electron entanglement data for opposite nuclear spin initialization.

a,b, As expected, for a nuclear spin-⇑-initialised state, varying the nuclear and electron projection phases ϕn, ϕe respectively, we observe oscillations with opposite phase compared to those for a nuclear spin-⇓-initialised state, compare Fig. 3c, d. c, Accordingly, XX and YY projections have opposite parity, compare Fig. 3e.

Source data

Extended Data Fig. 5 Overview of nuclear coherence times.

Details and fitted values for all Ramsey and Hahn echo sequences performed on two 29Si nuclear spins, one in quantum dot QD1, one in QD2, for different charge states. Ramsey values are fits to a sinusoidal function with envelope decay ~exp[-(τ/ T2*)α]. Int. time indicates total integration time for the measurement. Hahn echo values are fits to an exponential decay ~exp(−2τ/ T2Hahn). Figure panels displaying each measurement are indicated. Note that for the T2*-values given in the captions of Fig. 2 and Extended Data Figs. 2,3, the integration times are all limited to 1 hour, for comparison.

Supplementary information

Supplementary Information

Supplementary Figs. 1–3 and Notes 1 and 2.

Source data

Source Data Fig. 1

Numerical data used to generate graphs

Source Data Fig. 2

Numerical data used to generate graphs

Source Data Fig. 3

Numerical data used to generate graphs

Source Data Fig. 4

Numerical data used to generate graphs

Source Data Extended Data Fig. 1

Numerical data used to generate graphs

Source Data Extended Data Fig. 2

Numerical data used to generate graphs

Source Data Extended Data Fig. 3

Numerical data used to generate graphs

Source Data Extended Data Fig. 4

Numerical data used to generate graphs

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hensen, B., Wei Huang, W., Yang, CH. et al. A silicon quantum-dot-coupled nuclear spin qubit. Nat. Nanotechnol. 15, 13–17 (2020). https://doi.org/10.1038/s41565-019-0587-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41565-019-0587-7

This article is cited by

Search

Advanced 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