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. 2024 Jun 11;15:4977. doi: 10.1038/s41467-024-49182-4

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© The Author(s) 2024

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 4 — a 3D visualization of the manipulation zone consisting of two joined QuBus elements and two micromagnets. Shown is an exemplary two-qubit operation. b Cross-section including the gate layout showing the required magnetic field gradients for single- and two-qubit gates along the manipulation zone. The orange circle shows the position of the qubit during the single-qubit gate operation and is driven periodically in the region of a large perpendicular magnetic field gradient ∣∂_xB_⊥∣. The red and blue circles indicate the positions of the qubits during the two-qubit gate operations, respectively. Both are pushed together at the location of a large parallel magnetic field gradient ∣∂_xB_∥∣. c Potential line cuts showing the smooth formation of a tunnel-coupled double quantum dot potential appropriate for two-qubit operations as the two translated quantum dots approach the center of the manipulation zone. The color-coded bars correspond to the gates from panels a and b, and their vertical positions indicate the applied voltage V_i.