An addressable quantum dot qubit with fault-tolerant control-fidelity

Abstract

Exciting progress towards spin-based quantum computing1,2 has recently been made with qubits realized using nitrogen-vacancy centres in diamond and phosphorus atoms in silicon3. For example, long coherence times were made possible by the presence of spin-free isotopes of carbon4 and silicon5. However, despite promising single-atom nanotechnologies6, there remain substantial challenges in coupling such qubits and addressing them individually. Conversely, lithographically defined quantum dots have an exchange coupling that can be precisely engineered1, but strong coupling to noise has severely limited their dephasing times and control fidelities. Here, we combine the best aspects of both spin qubit schemes and demonstrate a gate-addressable quantum dot qubit in isotopically engineered silicon with a control fidelity of 99.6%, obtained via Clifford-based randomized benchmarking and consistent with that required for fault-tolerant quantum computing7,8. This qubit has dephasing time T2* = 120 μs and coherence time T2 = 28 ms, both orders of magnitude larger than in other types of semiconductor qubit. By gate-voltage-tuning the electron g*-factor we can Stark shift the electron spin resonance frequency by more than 3,000 times the 2.4 kHz electron spin resonance linewidth, providing a direct route to large-scale arrays of addressable high-fidelity qubits that are compatible with existing manufacturing technologies.

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References

1. 1

Loss, D. & DiVincenzo, D. P. Quantum computation with quantum dots. Phys. Rev. A 57, 120–126 (1998).

2. 2

DiVincenzo, D. P. The physical implementation of quantum computation. Fortschr. Phys. 48, 771–783 (2000).

3. 3

Awschalom, D. D., Bassett, L. C., Dzurak, A. S., Hu, E. L. & Petta, J. R. Quantum spintronics: engineering and manipulating atom-like spins in semiconductors. Science 339, 1174–1179 (2012).

4. 4

Bar-Gill, N., Pham, L. M., Jarmola, A., Budker, D. & Walsworth, R. L. Solid-state electronic spin coherence time approaching one second. Nature Commun. 4, 1743 (2013).

5. 5

Tyryshkin, A. M. et al. Electron spin coherence exceeding seconds in high-purity silicon. Nature Mater 11, 143–147 (2012).

6. 6

Fuechsle, M. et al. A single-atom transistor. Nature Nanotech. 7, 242–246 (2012).

7. 7

Knill, E. Quantum computing with realistically noisy devices. Nature 434, 39–44 (2005).

8. 8

Fowler, A., Marlantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 1–48 (2012).

9. 9

Petta, J. R. et al. Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180–2184 (2005).

10. 10

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

11. 11

Shulman, M. D. et al. Demonstration of entanglement of electrostatically coupled singlet–triplet qubits. Science 336, 202–205 (2012).

12. 12

Koppens, F. H. L., Nowack, K. C. & Vandersypen, L. M. K. Spin echo of a single electron spin in a quantum dot. Phys. Rev. Lett. 100, 236802 (2008).

13. 13

Bluhm, H., Foletti, S., Mahalu, D., Umansky, V. & Yacoby, A. Enhancing the coherence of a spin qubit by operating it as a feedback loop that controls its nuclear spin bath. Phys. Rev. Lett. 105, 216803 (2010).

14. 14

Maune, B. M. et al. Coherent singlet–triplet oscillations in a silicon-based double quantum dot. Nature 481, 344–347 (2012).

15. 15

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).

16. 16

Büch, H., Mahapatra, S., Rahman, R., Morello, A. & Simmons, M. Y. Spin readout and addressability of phosphorus-donor clusters in silicon. Nature Commun. 4, 2017 (2013).

17. 17

Nadj-Perge, S., Frolov, S. M., Bakkers, E. P. A. M. & Kouwenhoven, L. P. Spin–orbit qubit in a semiconductor nanowire. Nature 468, 1084–1087 (2010).

18. 18

Rahman, R. et al. Gate-induced g-factor control and dimensional transition for donors in multivalley semiconductors. Phys. Rev. B 80, 155301 (2009).

19. 19

Angus, S. J., Ferguson, A. J., Dzurak, A. S. & Clark, R. G. Gate-defined quantum dots in intrinsic silicon. Nano Lett. 7, 2051–2055 (2007).

20. 20

Fukatsu, S. et al. Effect of the Si/SiO2 interface on self-diffusion of Si in semiconductor-grade SiO2 . Appl. Phys. Lett. 83, 3897–3899 (2003).

21. 21

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

22. 22

Yang, C. H., Lim, W. H., Zwanenburg, F. A. & Dzurak, A. S. Dynamically controlled charge sensing of a few-electron silicon quantum dot. AIP Adv. 1, 042111 (2011).

23. 23

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

24. 24

Koppens, F. H. L. et al. Driven coherent oscillations of a single electron spin in a quantum dot. Nature 442, 766–771 (2006).

25. 25

Knill, E. et al. Randomized benchmarking of quantum gates. Phys. Rev. A 77, 012307 (2008).

26. 26

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

27. 27

Hao, X., Ruskov, R., Xiao, M., Tahan, C. & Jian, H. W. Electron spin resonance and spin-valley physics in a silicon double quantum dot. Nature Commun. 5, 3860 (2014).

28. 28

Bradbury, F. R. et al. Stark tuning of donor electron spins in silicon. Phys. Rev. Lett. 97, 176404 (2006).

29. 29

Muhonen, J. T. et al. Storing quantum information for 30 seconds in a nanoelectronic device. Preprint at http://arXiv.org/abs/1402.7140 (2014).

30. 30

Kalra, R., Laucht, A., Hill, C. D. & Morello, A. Robust two-qubit gates for donors in silicon controlled by hyperfine interactions. Phys. Rev. X 4, 021044 (2014).

Acknowledgements

The authors thank D. J. Reilly and J. R. Petta for discussions. The authors acknowledge support from the Australian Research Council (CE11E0096), the US Army Research Office (W911NF-13-1-0024) and the NSW Node of the Australian National Fabrication Facility. M.V. acknowledges support from the Netherlands Organization for Scientific Research (NWO) through a Rubicon Grant. The work at Keio has been supported in part by FIRST, the Core-to-Core Program by JSPS, and the Grant-in-Aid for Scientific Research and Project for Developing Innovation Systems by MEXT.

Author information

Authors

Contributions

M.V., J.C.C.H., C.H.Y., A.W.L., B.R., J.P.D. and J.T.M. performed the experiments. M.V. and F.E.H. fabricated the devices. K.M.I. prepared and supplied the 28Si epilayer wafer. M.V., C.H.Y., A.M. and A.S.D. designed the experiments and analysed the results. M.V. and A.S.D. wrote the manuscript, with input from all authors.

Corresponding authors

Correspondence to M. Veldhorst or A. S. Dzurak.

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Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary Information (PDF 752 kb)

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Veldhorst, M., Hwang, J., Yang, C. et al. An addressable quantum dot qubit with fault-tolerant control-fidelity. Nature Nanotech 9, 981–985 (2014). https://doi.org/10.1038/nnano.2014.216

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