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A silicon quantum-dot-coupled nuclear spin qubit

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

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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.

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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.

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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.

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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

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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.

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

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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.

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Source Data Fig. 1

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Source Data Fig. 3

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Source Data Fig. 4

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Source Data Extended Data Fig. 1

Numerical data used to generate graphs

Source Data Extended Data Fig. 2

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Source Data Extended Data Fig. 3

Numerical data used to generate graphs

Source Data Extended Data Fig. 4

Numerical data used to generate graphs

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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

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