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Coherent control of individual electron spins in a two-dimensional quantum dot array

Nature Nanotechnology volume 16, pages 296–301 (2021)Cite this article

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Abstract

The coherent manipulation of individual quantum objects organized in arrays is a prerequisite to any scalable quantum information platform. The cumulated efforts to control electron spins in quantum dot arrays have permitted the recent realization of quantum simulators and multielectron spin-coherent manipulations. Although a natural path to resolve complex quantum-matter problems and to process quantum information, two-dimensional (2D) scaling with a high connectivity of such implementations remains undemonstrated. Here we demonstrate the 2D coherent control of individual electron spins in a 3 × 3 array of tunnel-coupled quantum dots. We focus on several key quantum functionalities: charge-deterministic loading and displacement, local spin readout and local coherent exchange manipulation between two electron spins trapped in adjacent dots. This work lays some of the foundations to exploit a 2D array of electron spins for quantum simulation and information processing.

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Fig. 1: 2D array of QDs in the isolated regime.
Fig. 2: Single-electron charge configurations in the 3 × 3 array of QDs.
Fig. 3: Multiple electron charge configurations in the 3 × 3 array of QDs.
Fig. 4: Spin initialization, readout and manipulation in the QD array.
Fig. 5: Spin-mixing maps of the 2D array of five QDs.
Fig. 6: Local coherent exchange oscillations in the QD array.

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Data availability

All data underlying this study are available from the Zenodo repository at https://doi.org/10.5281/zenodo.4090905. Source data are provided with this paper.

References

  1. Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493 (1995).

    Article  CAS  Google Scholar 

  2. Bacon, D. Operator quantum error-correcting subsystems for self-correcting quantum memories. Phys. Rev. A 73, 012340 (2006).

    Article  Google Scholar 

  3. Fowler, A. G. Two-dimensional color-code quantum computation. Phys. Rev. A 83, 042310 (2011).

    Article  Google Scholar 

  4. Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).

    Article  Google Scholar 

  5. Dagotto, E. & Rice, T. M. Surprises on the way from one- to two-dimensional quantum magnets: the ladder materials. Science 271, 618–623 (1996).

    Article  CAS  Google Scholar 

  6. Veldhorst, M., Eenink, H. G. J., Yang, C. H. & Dzurak, A. S. Silicon CMOS architecture for a spin-based quantum computer. Nat. Commun. 8, 1766 (2017).

    Article  CAS  Google Scholar 

  7. Vandersypen, L. M. K. et al. Interfacing spin qubits in quantum dots and donors-hot, dense, and coherent. npj Quant. Inf. 3, 34 (2017).

    Article  Google Scholar 

  8. Ito, T. et al. Detection and control of charge states in a quintuple quantum dot. Sci. Rep. 6, 39113 (2016).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  10. Volk, C. et al. Loading a quantum-dot based ‘qubyte’ register. npj Quant. Inf. 5, 29 (2019).

    Article  Google Scholar 

  11. Hensgens, T. et al. Quantum simulation of a Fermi–Hubbard model using a semiconductor quantum dot array. Nature 548, 70–73 (2017).

    Article  CAS  Google Scholar 

  12. Dehollain, J. P. et al. Nagaoka ferromagnetism observed in a quantum dot plaquette. Nature 579, 528–533 (2020).

    Article  CAS  Google Scholar 

  13. Thalineau, R. et al. A few-electron quadruple quantum dot in a closed loop. Appl. Phys. Lett. 101, 103102 (2012).

    Article  Google Scholar 

  14. Mukhopadhyay, U., Dehollain, J. P., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. A 2 × 2 quantum dot array with controllable inter-dot tunnel couplings. Appl. Phys. Lett. 112, 183505 (2018).

    Article  Google Scholar 

  15. Bertrand, B. et al. Quantum manipulation of two-electron spin states in isolated double quantum dots. Phys. Rev. Lett. 115, 096801 (2015).

    Article  Google Scholar 

  16. Flentje, H. et al. A linear triple quantum dot system in isolated configuration. Appl. Phys. Lett. 110, 233101 (2017).

    Article  Google Scholar 

  17. Flentje, H. et al. Coherent long-distance displacement of individual electron spins. Nat. Commun. 8, 501 (2017).

    Article  CAS  Google Scholar 

  18. Baart, T. A., Jovanovic, N., Reichl, C., Wegscheider, W. & Vandersypen, L. M. K. Nanosecond-timescale spin transfer using individual electrons in a quadruple-quantum-dot device. Appl. Phys. Lett. 109, 043101 (2016).

    Article  Google Scholar 

  19. Bertrand, B. et al. Fast spin information transfer between distant quantum dots using individual electrons. Nat. Nanotechnol. 11, 672–676 (2016).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  22. Reed, M. et al. Reduced sensitivity to charge noise in semiconductor spin qubits via symmetric operation. Phys. Rev. Lett. 116, 110402 (2016).

    Article  CAS  Google Scholar 

  23. 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  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  27. Qiao, H. et al. Coherent multispin exchange coupling in a quantum-dot spin chain. Phys. Rev. X 10, 031006 (2020).

    CAS  Google Scholar 

  28. Hill, C. D. et al. A surface code quantum computer in silicon. Sci. Adv. 1, e1500707 (2015).

    Article  Google Scholar 

  29. Li, R. et al. A crossbar network for silicon quantum dot qubits. Sci. Adv. 4, eaar3960 (2018).

    Article  Google Scholar 

  30. Vinet, M. et al. Towards scalable silicon quantum computing. In 2018 IEEE International Electron Devices Meeting (IEDM) 6.5.1–6.5.4 (IEEE, 2018).

  31. Brunet, L. et al. First demonstration of a CMOS over CMOS 3D VISI CoolCube integration on 300 mm wafers. In 2016 IEEE Symposium on VLSI Technology 1–2 (IEEE, 2016).

  32. Chanrion, E. et al. Charge detection in an array of CMOS quantum dots. Phys. Rev. Appl. 14, 024066 (2020).

    Article  CAS  Google Scholar 

  33. Zwolak, J. P. et al. Autotuning of double-dot devices in situ with machine learning. Phys. Rev. Appl. 13, 034075 (2020).

    Article  CAS  Google Scholar 

  34. Hanson, R. et al. Single-shot read-out of electron spin states in a quantum dot using spin-dependent tunnel rates. Phys. Rev. Lett. 94, 196802 (2005).

    Article  CAS  Google Scholar 

  35. Meunier, T. et al. Experimental signature of phonon-mediated spin relaxation in a two-electron quantum dot. Phys. Rev. Lett. 98, 126601 (2007).

    Article  CAS  Google Scholar 

  36. Bautze, T. et al. Theoretical, numerical, and experimental study of a flying qubit electronic interferometer. Phys. Rev. B 89, 125432 (2014).

    Article  Google Scholar 

Download references

Acknowledgements

We thank M. Vinet, X. Hu and L. M. K. Vandersypen for enlightening discussions. We acknowledge technical support from the Pole groups of the Institut Néel, and in particular, the NANOFAB team who helped with the sample realization, as well as E. Eyraud, T. Crozes, P. Perrier, G. Pont, H. Rodenas, D. Lepoittevin, C. Hoarau and C. Guttin. M.U. acknowledges the support of project CODAQ (ANR-16-ACHN-0029). A.L. and A.D.W. acknowledge the support of DFG-TRR160, BMBF-Q.com-H 16KIS0109 and DFH/UFA CDFA-05-06. T.M. acknowledges financial support from ERC QSPINMOTION, ERC QUCUBE, ANR CMOSQSPIN (Grant no. ANR-17-CE24-0009), ANR SiQuBus and UGA IDEX (Grant no. ANR-15-IDEX-02).

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Authors and Affiliations

  1. Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, Grenoble, France

    Pierre-André Mortemousque, Emmanuel Chanrion, Baptiste Jadot, Hanno Flentje, Matias Urdampilleta, Christopher Bäuerle & Tristan Meunier

  2. Université Grenoble Alpes, CEA, Leti, Grenoble, France

    Pierre-André Mortemousque

  3. Lehrstuhl für Angewandte Festkörperphysik, Ruhr-Universität Bochum, Bochum, Germany

    Arne Ludwig & Andreas D. Wieck

Authors
  1. Pierre-André Mortemousque
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Contributions

P.-A.M. fabricated the sample and performed the experiments with the help of T.M. and C.B. P.-A.M. and T.M. interpreted the data. P.-A.M. and T.M. wrote the manuscript with input from all the other authors. H.F. contributed to the experimental set-up. A.L. and A.D.W. performed the design and molecular-beam-epitaxy growth of the high-mobility heterostructure. All the authors discussed the results extensively, as well as the manuscript.

Corresponding authors

Correspondence to Pierre-André Mortemousque or Tristan Meunier.

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The authors declare no competing interests.

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Peer review information Nature Nanotechnology thanks the anonymous reviewers for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–9, and Tables 1–3.

Source data

Source Data Fig. 1

Numerical data used to generate graphs in Figure 1.

Source Data Fig. 2

Numerical data used to generate graphs in Figure 2.

Source Data Fig. 3

Numerical data used to generate graphs in Figure 3.

Source Data Fig. 4

Numerical data used to generate graphs in Figure 4.

Source Data Fig. 5

Numerical data used to generate graphs in Figure 5.

Source Data Fig. 6

Numerical data used to generate graphs in Figure 6.

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Mortemousque, PA., Chanrion, E., Jadot, B. et al. Coherent control of individual electron spins in a two-dimensional quantum dot array. Nat. Nanotechnol. 16, 296–301 (2021). https://doi.org/10.1038/s41565-020-00816-w

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