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A singlet-triplet hole spin qubit in planar Ge


Spin qubits are considered to be among the most promising candidates for building a quantum processor. Group IV hole spin qubits are particularly interesting owing to their ease of operation and compatibility with Si technology. In addition, Ge offers the option for monolithic superconductor–semiconductor integration. Here, we demonstrate a hole spin qubit operating at fields below 10 mT, the critical field of Al, by exploiting the large out-of-plane hole g-factors in planar Ge and by encoding the qubit into the singlet-triplet states of a double quantum dot. We observe electrically controlled g-factor difference-driven and exchange-driven rotations with tunable frequencies exceeding 100 MHz and dephasing times of 1 μs, which we extend beyond 150 μs using echo techniques. These results demonstrate that Ge hole singlet-triplet qubits are competing with state-of-the-art GaAs and Si singlet-triplet qubits. In addition, their rotation frequencies and coherence are comparable with those of Ge single spin qubits, but singlet-triplet qubits can be operated at much lower fields, emphasizing their potential for on-chip integration with superconducting technologies.

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Fig. 1: Heterostructure and gate layout.
Fig. 2: Pauli spin blockade and dispersion relation.
Fig. 3: Δg-driven rotations.
Fig. 4: Exchange-rotations at B = 1 mT and VCB = 910 mV.
Fig. 5: Spin echo at B = 1 mT.

Data availability

All data included in this work are available from the Institute of Science and Technology Austria repository47.


  1. 1.

    Scappucci, G. et al. The germanium quantum information route. Nat. Rev. Mater. (2020).

  2. 2.

    Kloeffel, C., Trif, M. & Loss, D. Strong spin-orbit interaction and helical hole states in Ge/Si nanowires. Phys. Rev. B 84, 195314 (2011).

    Article  CAS  Google Scholar 

  3. 3.

    Froning, F. N. M. et al. Ultrafast hole spin qubit with gate-tunable spin–orbit switch functionality. Nat. Nanotechnol. 16, 308–312 (2021).

    CAS  Article  Google Scholar 

  4. 4.

    Wang, Z. et al. Optimal operation points for ultrafast, highly coherent Ge hole spin-orbit qubits. npj Quantum Inf. 7, 54 (2021).

    Article  Google Scholar 

  5. 5.

    Lodari, M. et al. Light effective hole mass in undoped Ge/SiGe quantum wells. Phys. Rev. B 100, 041304(R) (2019).

    Article  Google Scholar 

  6. 6.

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

    CAS  Article  Google Scholar 

  7. 7.

    Hendrickx, N. W. et al. A four-qubit germanium quantum processor. Nature 591, 580–585 (2021).

    Article  CAS  Google Scholar 

  8. 8.

    Watzinger, H. et al. A germanium hole spin qubit. Nat. Commun. 9, 3902 (2018).

    Article  CAS  Google Scholar 

  9. 9.

    Hendrickx, N. W., Franke, D. P., Sammak, A., Scappucci, G. & Veldhorst, M. Fast two-qubit logic with holes in germanium. Nature 577, 487–491 (2020).

    CAS  Article  Google Scholar 

  10. 10.

    Katsaros, G. et al. Observation of spin-selective tunneling in SiGe nanocrystals. Phys. Rev. Lett. 107, 246601 (2011).

    CAS  Article  Google Scholar 

  11. 11.

    Levy, J. Universal quantum computation with spin-1/2 pairs and Heisenberg exchange. Phys. Rev. Lett. 89, 147902 (2002).

    Article  CAS  Google Scholar 

  12. 12.

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

    CAS  Article  Google Scholar 

  13. 13.

    Petta, J. R., Lu, H. & Gossard, A. C. A coherent beam splitter for electronic spin states. Science 327, 669–672 (2010).

    CAS  Article  Google Scholar 

  14. 14.

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

    CAS  Article  Google Scholar 

  15. 15.

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

    CAS  Article  Google Scholar 

  16. 16.

    Wu, X. et al. Two-axis control of a singlet-triplet qubit with an integrated micromagnet. Proc. Natl Acad. Sci. USA 111, 11938–11942 (2014).

    CAS  Article  Google Scholar 

  17. 17.

    Takeda, K., Noiri, A., Yoneda, J., Nakajima, T. & Tarucha, S. Resonantly driven singlet-triplet spin qubit in silicon. Phys. Rev. Lett. 124, 117701 (2020).

    CAS  Article  Google Scholar 

  18. 18.

    Jock, R. M. et al. A silicon metal-oxide-semiconductor electron spin-orbit qubit. Nat. Commun. 9, 1768 (2018).

    Article  CAS  Google Scholar 

  19. 19.

    Harvey-Collard, P. et al. Spin-orbit interactions for singlet-triplet qubits in silicon. Phys. Rev. Lett. 122, 217702 (2019).

    CAS  Article  Google Scholar 

  20. 20.

    Watzinger, H. et al. Heavy-hole states in germanium hut wires. Nano Lett. 16, 6879–6885 (2016).

    CAS  Article  Google Scholar 

  21. 21.

    Hofmann, A. et al. Assessing the potential of Ge/SiGe quantum dots as hosts for singlet-triplet qubits. Preprint at (2019).

  22. 22.

    Liles, S. D. et al. Spin and orbital structure of the first six holes in a silicon metal-oxide-semiconductor quantum dot. Nat. Commun. 9, 3255 (2018).

    CAS  Article  Google Scholar 

  23. 23.

    Barthel, C. et al. Relaxation and readout visibility of a singlet-triplet qubit in an Overhauser field gradient. Phys. Rev. B 85, 035306 (2012).

    Article  CAS  Google Scholar 

  24. 24.

    Studenikin, S. A. et al. Enhanced charge detection of spin qubit readout via an intermediate state. Appl. Phys. Lett. 101, 233101 (2012).

    Article  CAS  Google Scholar 

  25. 25.

    Orona, L. A. et al. Readout of singlet-triplet qubits at large magnetic field gradients. Phys. Rev. B 98, 125404 (2018).

    CAS  Article  Google Scholar 

  26. 26.

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

    Article  CAS  Google Scholar 

  27. 27.

    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 (2017).

    Article  CAS  Google Scholar 

  28. 28.

    Moon, H. et al. Machine learning enables completely automatic tuning of a quantum device faster than human experts. Nat. Commun. 11, 4161 (2020).

    CAS  Article  Google Scholar 

  29. 29.

    Shulman, M. D. et al. Suppressing qubit dephasing using real-time Hamiltonian estimation. Nat. Commun. 5, 5156 (2014).

    CAS  Article  Google Scholar 

  30. 30.

    Bluhm, H. et al. Dephasing time of GaAs electron-spin qubits coupled to a nuclear bath exceeding 200 μs. Nat. Phys. 7, 109–113 (2010).

    Article  CAS  Google Scholar 

  31. 31.

    Cerfontaine, P. et al. Closed-loop control of a GaAs-based singlet-triplet spin qubit with 99.5% gate fidelity and low leakage. Nat. Commun. 11, 4144 (2020).

    CAS  Article  Google Scholar 

  32. 32.

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

    Article  CAS  Google Scholar 

  33. 33.

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

    CAS  Article  Google Scholar 

  34. 34.

    Nichol, J. M. et al. High-fidelity entangling gate for double-quantum-dot spin qubits. npj Quantum Inf. 3 3 (2017).

  35. 35.

    Wallraff, A. et al. Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics. Nature 431, 162–167 (2004).

    CAS  Article  Google Scholar 

  36. 36.

    Stehlik, J. et al. Fast charge sensing of a cavity-coupled double quantum dot using a Josephson parametric amplifier. Phys. Rev. Appl. 4, 014018 (2015).

    Article  CAS  Google Scholar 

  37. 37.

    Burkard, G., Gullans, M. J., Mi, X. & Petta, J. R. Superconductor–semiconductor hybrid-circuit quantum electrodynamics. Nat. Rev. Phys. 2, 129–140 (2020).

    Article  Google Scholar 

  38. 38.

    Leonard, E. et al. Digital coherent control of a superconducting qubit. Phys. Rev. Appl. 11, 014009 (2019).

    CAS  Article  Google Scholar 

  39. 39.

    Schupp, F. J. et al. Sensitive radiofrequency readout of quantum dots using an ultra-low-noise SQUID amplifier. J. Appl. Phys. 127, 244503 (2020).

    CAS  Article  Google Scholar 

  40. 40.

    Vigneau, F. et al. Germanium quantum-well Josephson field-effect transistors and interferometers. Nano Lett. 19, 1023–1027 (2019).

    Article  CAS  Google Scholar 

  41. 41.

    Amitonov, S. V., Spruijtenburg, P. C., Vervoort, M. W. S., van der Wiel, W. G. & Zwanenburg, F. A. Depletion-mode quantum dots in intrinsic silicon. Appl. Phys. Lett. 112, 023102 (2018).

    Article  CAS  Google Scholar 

  42. 42.

    Rössner, B., Chrastina, D., Isella, G. & von Känel, H. Scattering mechanisms in high-mobility strained Ge channels. Appl. Phys. Lett. 84, 3058–3060 (2004).

    Article  CAS  Google Scholar 

  43. 43.

    Shah, V. A. et al. Reverse graded relaxed buffers for high Ge content SiGe virtual substrates. Appl. Phys. Lett. 93, 192103 (2008).

    Article  CAS  Google Scholar 

  44. 44.

    Wang, Z. et al. Optimal operation points for ultrafast, highly coherent Ge hole spin-orbit qubits. Preprint at https://arXiv:1911.11143 (2019).

  45. 45.

    Sammak, A. et al. Shallow and undoped germanium quantum wells: a playground for spin and hybrid quantum technology. Adv. Funct. Mater. 29, 1807613 (2019).

    Article  CAS  Google Scholar 

  46. 46.

    Marchionna, S., Virtuani, A., Acciarri, M., Isella, G. & von Kaenel, H. Defect imaging of SiGe strain relaxed buffers grown by LEPECVD. Mater. Sci. Semicond. Process. 9, 802–805 (2006).

    CAS  Article  Google Scholar 

  47. 47.

    Jirovec, D. Research data for “A singlet-triplet hole spin qubit planar Ge”. (2021).

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This research was supported by the Scientific Service Units of Institute of Science and Technology (IST) Austria through resources provided by the Miba Machine Shop and the nanofabrication facility, and was made possible with the support of the NOMIS Foundation. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Sklodowska-Curie grant agreements no. 844511 and no. 75441, and by the Austrian Science Fund FWF-P 30207 project. A.B. acknowledges support from the European Union Horizon 2020 FET project microSPIRE, no. 766955. M. Botifoll and J.A. acknowledge funding from Generalitat de Catalunya 2017 SGR 327. The Catalan Institute of Nanoscience and Nanotechnology (ICN2) is supported by the Severo Ochoa programme from the Spanish Ministery of Economy (MINECO) (grant no. SEV-2017-0706) and is funded by the Catalonian Research Centre (CERCA) Programme, Generalitat de Catalunya. Part of the present work has been performed within the framework of the Universitat Autónoma de Barcelona Materials Science PhD programme. Part of the HAADF scanning transmission electron microscopy was conducted in the Laboratorio de Microscopias Avanzadas at Instituto de Nanociencia de Aragon, Universidad de Zaragoza. ICN2 acknowledge support from the Spanish Superior Council of Scientific Research (CSIC) Research Platform on Quantum Technologies PTI-001. M.B. acknowledges funding from the Catalan Agency for Management of University and Research Grants (AGAUR) Generalitat de Catalunya formation of investigators (FI) PhD grant.

Author information




D.J. fabricated the sample and performed the experiments and data analysis. D.J., A.H. and I.P. developed the fabrication recipe. D.J., A.H., O.S. and M. Borovkov performed precharacterizing measurements on equivalent samples. J.S.-M. and G.K. fabricated the two additional devices discussed in the Supplementary Information. J.K. performed the experiments on those additional devices. D.C. and A.B. designed the SiGe heterostructure. A.B. performed the growth, supervised by G.I.; D.C. performed the X-ray diffraction measurements and simulations. G.T. performed Hall effect measurements, supervised by D.C.; P.M.M. derived the theoretical model. M. Botifoll and J.A. performed the atomic resolution scanning transmission electron microscopy structural and electron energy-loss spectroscopy compositional related characterization and calculated the strain by using geometrical phase analysis. D.J., A.H., J.K., A.C., F.M., J.S.-M. and G.K. discussed the qubit data. D.J. and G.K. wrote the manuscript with input from all the authors. G.I. and G.K. initiated and supervised the project.

Corresponding authors

Correspondence to Daniel Jirovec or Georgios Katsaros.

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The authors declare no competing interests.

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Peer review information Nature Materials thanks Guo-Ping Guo, Yinyu Liu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–20 and Discussion.

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Jirovec, D., Hofmann, A., Ballabio, A. et al. A singlet-triplet hole spin qubit in planar Ge. Nat. Mater. (2021).

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