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A two-qubit gate between phosphorus donor electrons in silicon

Nature volume 571, pages 371–375 (2019)Cite this article

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Abstract

Electron spin qubits formed by atoms in silicon have large (tens of millielectronvolts) orbital energies and weak spin–orbit coupling, giving rise to isolated electron spin ground states with coherence times of seconds1,2. High-fidelity (more than 99.9 per cent) coherent control of such qubits has been demonstrated3, promising an attractive platform for quantum computing. However, inter-qubit coupling—which is essential for realizing large-scale circuits in atom-based qubits—has not yet been achieved. Exchange interactions between electron spins4,5 promise fast (gigahertz) gate operations with two-qubit gates, as recently demonstrated in gate-defined silicon quantum dots6,7,8,9,10. However, creating a tunable exchange interaction between two electrons bound to phosphorus atom qubits has not been possible until now. This is because it is difficult to determine the atomic distance required to turn the exchange interaction on and off while aligning the atomic circuitry for high-fidelity, independent spin readout. Here we report a fast (about 800 picoseconds) \(\sqrt{{\bf{SWAP}}}\) two-qubit exchange gate between phosphorus donor electron spin qubits in silicon using independent single-shot spin readout with a readout fidelity of about 94 per cent on a complete set of basis states. By engineering qubit placement on the atomic scale, we provide a route to the realization and efficient characterization of multi-qubit quantum circuits based on donor qubits in silicon.

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Fig. 1: High-fidelity, independent single-shot spin readout of two donor qubits.
Fig. 2: Electrostatic control over the electron-exchange interaction.
Fig. 3: Exchange-driven coherent spin–spin oscillations.
Fig. 4: Two-qubit SWAP gate with truth table.

Data availability

The data pertaining to this study are available from the corresponding author upon reasonable request.

References

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  3. Muhonen, J. T. et al. Quantifying the quantum gate fidelity of single-atom spin qubits in silicon by randomized benchmarking. J. Phys. Condens. Matter 27, 154205 (2015).

    Article  ADS  CAS  Google Scholar 

  4. Hill, C. D. et al. Global control and fast solid-state donor electron spin quantum computing. Phys. Rev. B 72, 045350 (2005).

    Article  ADS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  MathSciNet  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  9. Brunner, R. et al. Two-qubit gate of combined single-spin rotation and interdot spin exchange in a double quantum dot. Phys. Rev. Lett. 107, 146801 (2011).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  11. Meunier, T., Calado, V. E. & Vandersypen, L. M. K. Efficient controlled-phase gate for single-spin qubits in quantum dots. Phys. Rev. B 83, 121403 (2011).

    Article  ADS  Google Scholar 

  12. 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).

    Google Scholar 

  13. Hile, S. J. et al. Radio frequency reflectometry and charge sensing of a precision placed donor in silicon. Appl. Phys. Lett. 107, 093504 (2015).

    Article  ADS  Google Scholar 

  14. Weber, B. et al. Spin blockade and exchange in Coulomb-confined silicon double quantum dots. Nat. Nanotechnol. 9, 430–435 (2014).

    Article  ADS  CAS  Google Scholar 

  15. Yoneda, J. et al. A quantum-dot spin qubit with coherence limited by charge noise and fidelity higher than 99.9%. Nat. Nanotechnol. 13, 102–106 (2018).

    Article  ADS  CAS  Google Scholar 

  16. Dial, O. E. et al. Charge noise spectroscopy using coherent exchange oscillations in a singlet-triplet qubit. Phys. Rev. Lett. 110, 146804 (2013).

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  18. Broome, M. A. et al. High-fidelity single-shot singlet-triplet readout of precision-placed donors in silicon. Phys. Rev. Lett. 119, 046802 (2017).

    Article  ADS  CAS  Google Scholar 

  19. Broome, M. A. et al. Two-electron spin correlations in precision placed donors in silicon. Nat. Commun. 9, 980 (2018).

    Article  ADS  CAS  Google Scholar 

  20. Hsueh, Y.-L. et al. Spin-lattice relaxation times of single donors and donor clusters in silicon. Phys. Rev. Lett. 113, 246406 (2014).

    Article  ADS  Google Scholar 

  21. Koiller, B., Hu, X. & Das Sarma, S. Exchange in silicon-based quantum computer architecture. Phys. Rev. Lett. 88, 027903 (2001).

    Article  ADS  Google Scholar 

  22. Wang, Y. et al. Highly tunable exchange in donor qubits in silicon. npj Quantum Inf. 2, 16008 (2016).

    Article  ADS  Google Scholar 

  23. Wang, Y., Chen, C.-Y., Klimeck, G., Simmons, M. Y. & Rahman, R. Characterizing Si:P quantum dot qubits with spin resonance techniques. Sci. Rep. 6, 31830 (2016); corrigendum 6, 38120 (2016).

    Article  ADS  CAS  Google Scholar 

  24. Watson, T. F., Weber, B., House, M. G., Büch, H. & Simmons, M. Y. High-fidelity rapid initialization and read-out of an electron spin via the single donor D− charge state. Phys. Rev. Lett. 115, 166806 (2015).

    Article  ADS  CAS  Google Scholar 

  25. Watson, T. F. et al. Atomically engineered electron spin lifetimes of 30 s in silicon. Sci. Adv. 3, e1602811 (2017).

    Article  ADS  Google Scholar 

  26. Politi, A., Cryan, M. J., Rarity, J. G., Yu, S. & O’Brien, J. L. Silica-on-silicon waveguide quantum circuits. Science 320, 646–649 (2008).

    Article  ADS  CAS  Google Scholar 

  27. Abrosimov, N. V. et al. A new generation of 99.999% enriched 28Si single crystals for the determination of Avogadro’s constant. Metrologia 54, 599–609 (2017).

    Article  ADS  CAS  Google Scholar 

  28. Throckmorton, R. E., Barnes, E. & Das Sarma, S. Environmental noise effects on entanglement fidelity of exchange-coupled semiconductor spin qubits. Phys. Rev. B 95, 085405 (2017).

    Article  ADS  Google Scholar 

  29. Martins, F. et al. Noise suppression using symmetric exchange gates in spin qubits. Phys. Rev. Lett. 116, 116801 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  30. Wang, X. et al. Composite pulses for robust universal control of singlet–triplet qubits. Nat. Commun. 3, 997 (2012).

    Article  ADS  Google Scholar 

  31. Horibe, K., Kodera, T. & Oda, S. Back-action-induced excitation of electrons in a silicon quantum dot with a single-electron transistor charge sensor. Appl. Phys. Lett. 106, 053119 (2015).

    Article  ADS  Google Scholar 

  32. Shamim, S., Weber, B., Thompson, D. W., Simmons, M. Y. & Ghosh, A. Ultra low-noise atomic-scale structures for quantum circuitry in silicon. Nano Lett. 16, 5779–5784 (2016).

    Article  ADS  CAS  Google Scholar 

  33. Keizer, J. G., Koelling, S., Koenraad, P. M. & Simmons, M. Y. Suppressing segregation in highly phosphorus doped silicon monolayers. ACS Nano 9, 12537–12541 (2015).

    Article  CAS  Google Scholar 

  34. Gorman, S. K. et al. Tunneling statistics for analysis of spin-readout fidelity. Phys. Rev. Appl. 8, 034019 (2017).

    Article  ADS  Google Scholar 

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Acknowledgements

The research was supported by the Australian Research Council Centre of Excellence for Quantum Computation and Communication Technology (project number CE170100012), the US Army Research Office under contract number W911NF-17-1-0202 and Silicon Quantum Computing Pty Ltd. M.Y.S. acknowledges an Australian Research Council Laureate Fellowship. This work was performed in part at the NSW node of the Australian National Fabrication Facility.

Reviewer information

Nature thanks Benjamin D’Anjou and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Author notes

  1. These authors contributed equally: Y. He, S. K. Gorman

Authors and Affiliations

  1. Centre of Excellence for Quantum Computation and Communication Technology, School of Physics, University of New South Wales, Sydney, New South Wales, Australia

    Y. He, S. K. Gorman, D. Keith, L. Kranz, J. G. Keizer & M. Y. Simmons

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Contributions

Y.H., S.K.G. and L.K. fabricated the device. Y.H., S.K.G. and D.K. performed the measurements. Y.H., S.K.G., D.K, L.K. and J.G.K. analysed the data. The manuscript was written by Y.H., S.K.G. and M.Y.S. with input from all other authors. M.Y.S. conceived and supervised the project.

Corresponding author

Correspondence to M. Y. Simmons.

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Competing interests

M.Y.S. is a director of the company Silicon Quantum Computing Pty Ltd.

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Extended data figures and tables

Extended Data Fig. 1 Determination of the number of donors in a qubit from the quantum dot charging energies.

a, RF-SET Coulomb diamonds. b, Gate–gate map around the (1, 3) ↔ (2, 2) charge transition and definitions of \({\rm{\delta }}{V}_{{\rm{g}}}^{{\rm{D}}{\rm{D}}}\), \({\rm{\Delta }}{V}_{{\rm{g}}}^{{\rm{S}}}\), \({\rm{\delta }}{V}_{{\rm{g}}}^{{\rm{S}}}\) and \({\rm{\delta }}{V}_{{\rm{g}}}^{{\rm{D}}}\). c, Gate–gate map for the regime with two electrons on donor qubits and definition of \({\rm{\Delta }}{V}_{{\rm{g}}}^{{\rm{D}}}\).

Extended Data Fig. 2 Experimental set-up for the two-qubit gate in a millikelvin dilution refrigerator.

The schematic shows the electrical connections from the device to the control computer at the different temperature stages of the dilution refrigerator from the top to bottom. An STM image of the device attached to the cold finger of the refrigerator at 50 mK is shown in the lower orange pane. The RF-reflectormetry circuit attached to the device employs a variable attenuator (‘Var. Atten.’) to control the power coupled through a directional coupler (‘Dir. Cplr.’) and sent to the source contact of the SET (red lines). The blue line is for d.c. current/voltage measurements of the SET. The slow signals (black components) and fast signals (green components) are combined using bias tees at 50 mK before being sent to the left and right gate electrodes.

Supplementary information

Supplementary Information

This file contains Supplementary Information Sections 1–5, Supplementary Tables 1–3, Supplementary References and Supplementary Figures 1–4.

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He, Y., Gorman, S.K., Keith, D. et al. A two-qubit gate between phosphorus donor electrons in silicon. Nature 571, 371–375 (2019). https://doi.org/10.1038/s41586-019-1381-2

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