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# A singlet-triplet hole spin qubit in planar Ge

## Abstract

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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## Data availability

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

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## Acknowledgements

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

Authors

### Contributions

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.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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). https://doi.org/10.1038/s41563-021-01022-2