Abstract
Hole spins in silicon or germanium quantum dots have emerged as a capable platform for scalable solid-state quantum processors. In addition to benefiting from well-established manufacturing technologies, the large spin–orbit coupling of hole spin qubits enables fast control mediated by an electric field. Unfortunately, this coupling typically makes hole spin qubits susceptible to charge noise, which usually limits qubit coherence. Here we experimentally establish the existence of so-called sweet lines in the parameter space of field orientation where the qubit becomes insensitive to charge noise. We do this by varying the direction of a magnetic field applied to a silicon metal–oxide–semiconductor hole qubit. We also find that the observed sweet lines contain the points of maximal driving efficiency, in agreement with recent theoretical predictions. Furthermore, we show that moderate adjustments in gate voltages can substantially shift the sweet lines. This tunability allows several qubits to be simultaneously made insensitive to electrical noise, making it possible to design scalable qubit architectures that feature all-electrical spin control of many qubits.
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Data availability
All data underlying this study are available via Zenodo at https://doi.org/10.5281/zenodo.17378720 (ref. 40).
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Acknowledgements
This work is supported by the French National Research Agency under the programme France 2030 (PEPR PRESQUILE - ANR-22-PETQ-0002), by the European Union’s Horizon 2020 research innovation programme through projects QLSI1 and QLSI2 (Grant Agreement Nos. 951852 and 101135712, respectively) and the European Research Council project QuCube (Grant Agreement No. 810504). J.C.A.-U. is supported by Grant Nos. RYC2022-037527-I and PID2023-148257NA-I00 funded by MCIU/AEI/10.13039/501100011033 and by the ESF+. V.C. acknowledges support from the Program QuantForm-UGA ANR-21-CMAQ-0003 France 2030 and by the LabEx LANEF ANR-10-LABX-51-01.
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M.B., B. Brun, T.N., V.C. and V.S. performed the experiments with support from S.Z., R.M. and X.J. and advice from all co-authors. M.B, E.A.R.-M., J.C.A.-U., Y.-M.N. and V.S. performed the simulations and the data analysis. B. Bertrand and H.N. designed and supervised the fabrication of the device. M.B., E.A.R.-M., Y.-M.N., S.D.F. and V.S. co-wrote the paper with input from all co-authors. V.S. led the experiments. S.D.F. initiated the project.
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Extended data
Extended Data Fig. 1 Hole effective g-factor comparison between qubits Q3 and Q4.
Blue (red) points are g-factors measured by EDSR of Q3 (Q4). Solid lines are the fitted g-factors using the g-matrix formalism presented in Methods and Supplementary Section 2. The g-factor configuration presented for the qubit Q3 correspond to the left panel of Fig. 2. The tilt of the principal axes of the lobes with respect to the device axes is most likely due to inhomogeneous strains14,24,25.
Extended Data Fig. 2 Ramsey, Hahn-Echo coherence times and Rabi frequency measured in the sample plane.
a Ramsey coherence time (green points) plotted as a function of magnetic field angle θ in the sample plane. In red are depicted the absolute values of β∥(T3) and the corresponding fit presented in the main text. Dashed lines evidence the sweet-spot positions where the coherence time is expected to increase. b Inverse of Hahn-Echo coherence time plotted as a function of magnetic field direction in the sample plane (NP). The red solid line is the fit to ∣β∥(T3)∣ presented in the main text. c Rabi frequency variations according to magnetic field direction in the sample plane (NP). Red line and points (fit) represent ∣β∥(T3)∣. At the sweet-spot orientations two distinct cases are observed: one sweet spot with a fast electrical control (θ = − 20°) and the second one (θ = 35°) with a much slower Rabi frequency.
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Supplementary Sections I–V and Figs. 1–5.
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Bassi, M., Rodríguez-Mena, E.A., Brun, B. et al. Optimal operation of hole spin qubits. Nat. Phys. 22, 75–80 (2026). https://doi.org/10.1038/s41567-025-03106-1
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DOI: https://doi.org/10.1038/s41567-025-03106-1
