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arXiv:2512.19785

Micromagnet-free operation of electron spin qubits in Si/Si$_{1-x}$Ge$_x$ vertical double quantum dots

Abhikbrata Sarkar, Daniel Loss

cond-mat.mes-hallquant-phSubmitted Dec 22, 2025• Announced Dec 24, 2025
arXivHTMLPDF

Abstract

We study a vertical double quantum dot (DQD) in a Si/Si$_{1-x}$Ge$_x$/Si double-well heterostructure for full electrical control of electron Loss-DiVincenzo (LD) spin qubits, using realistic device modeling and numerical simulations. Due to the emerging spin-orbit interaction in the DQD, as well as strain from the gate electrodes, small (percentage range) but finite $g$ tensor variations emerge. In addition, we find a large valley splitting, on the order of $E_v{\sim}250\,μ$eV. As a result, multiple avenues for fast electrical single qubit rotations emerge. An ac electric field gives rise to electric dipole spin resonance (EDSR), while electron spin resonance (ESR) in the presence of an ac magnetic field can be electrically controlled by local gates due to varying $g$ factors in DQDs. We also show that shuttling between neighboring dots, in vertical and horizontal direction, results in ultrafast single qubit gates of less than a nanosecond. Remarkably, this DQD architecture completely eliminates the need for micromagnets, significantly facilitating the scalability of LD spin qubits in semiconductor foundries.

Journal reference
Phys. Rev. Research 8, 023232 (2026)
DOI
10.1103/rsnv-mnlw
Comments
4 pages, 4 figures

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We study a vertical double quantum dot (DQD) in a Si/Si1−x_{1-x}1−x​Gex_xx​/Si double-well heterostructure for full electrical control of electron Loss-DiVincenzo (LD) spin qubits, using realistic device modeling and numerical simulations. Due to the emerging spin-orbit interaction in the DQD, as well as strain from the gate electrodes, small (percentage range) but finite ggg tensor variations emerge. In addition, we find a large valley splitting, on the order of Ev∼250 μE_v{\sim}250\,μEv​∼250μeV. As a result, multiple avenues for fast electrical single qubit rotations emerge. An ac electric field gives rise to electric dipole spin resonance (EDSR), while electron spin resonance (ESR) in the presence of an ac magnetic field can be electrically controlled by local gates due to varying ggg factors in DQDs. We also show that shuttling between neighboring dots, in vertical and horizontal direction, results in ultrafast single qubit gates of less than a nanosecond. Remarkably, this DQD architecture completely eliminates the need for micromagnets, significantly facilitating the scalability of LD spin qubits in semiconductor foundries.
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Spin qubits in semiconductor quantum dots constitute one of the leading platforms for quantum information processing, combining long coherence times, high-fidelity gate operations, and compatibility with semiconductor industry technologies. In particular, holes confined in planar Ge/SiGe heterostructures have recently emerged as promising qubit candidates owing to their low effective mass, high mobility, low percolation density, absence of valley states, and strong spin-orbit interaction, which enables fast all-electrical spin control. At the same time, spin-orbit interaction also gives rise to a highly anisotropic and electrically tunable gyromagnetic response. Understanding and controlling this response is therefore essential for high-fidelity single- and multi-qubit operations. The realization of scalable quantum processors also requires efficient qubit readout and long-range connectivity. Circuit quantum electrodynamics (cQED), based on the coupling between artificial atoms and microwave photons confined in superconducting resonators, provides a natural framework to address these challenges. However, the implementation of hybrid semiconductor-superconductor devices in planar Ge has so far been hindered by large microwave losses originating from the heterostructure. In this thesis, we demonstrate, for the first time in planar Ge, strong coupling between a hole charge qubit in a double quantum dot and a high-impedance microwave resonator, reaching a cooperativity of C â 100. In addition, we leverage the frequency tunability of the resonator to perform detailed spectroscopy of a multi-level energy spectrum of low-lying states arising from strong Coulomb-correlation effects. To further improve the quality of the hole-photon interface, we investigate the source of microwave losses in different Ge/SiGe heterostructures, identifying defects at the lattice-mismatched Si/Ge interface as the dominant source of resonator losses in reverse-graded heterostructures. To mitigate this limitation, a deep tapered-etching approach is introduced, enabling the fabrication of superconducting resonators directly on etched heterostructures. This method yields internal quality factors exceeding Qint > 10 000 for high-impedance Josephson junction array resonators and Qint > 100 000 for 50 â Nb resonators. Finally, this thesis explores the spin properties of multi-hole quantum dots beyond the conventional single-orbital picture. By reconstructing and electrically tuning the g tensors of holes confined in different orbital states, we show that confinement can substantially modify both their magnitude and orientation. These results open new opportunities for engineering qubit properties through orbital occupation. Furthermore, highly coherent singlet-triplet oscillations are demonstrated in the seven-hole regime, yielding a quality factor of approximately 330 at in-plane magnetic fields as low as 2.5 mT. Together, these results establish a foundation for high-fidelity hole-spin-qubit operation based on g-tensor engineering and for the integration of planar Ge quantum dots with superconducting quantum circuits.
We propose a setup for universal and electrically controlled quantum information processing with hole spins in Ge/Si core/shell nanowire quantum dots (NW QDs). Single-qubit gates can be driven through electric-dipole-induced spin resonance, with spin-flip times shorter than 100 ps. Long-distance qubit-qubit coupling can be mediated by the cavity electric field of a superconducting transmission line resonator, where we show that operation times below 20 ns seem feasible for the entangling iSWAP\sqrt{i\text{SWAP}}iSWAP​ gate. The absence of Dresselhaus spin-orbit interaction (SOI) and the presence of an unusually strong Rashba-type SOI enable precise control over the transverse qubit coupling via an externally applied, perpendicular electric field. The latter serves as an on-off switch for quantum gates and also provides control over the ggg factor, so single- and two-qubit gates can be operated independently. Remarkably, we find that idle qubits are insensitive to charge noise and phonons, and we discuss strategies for enhancing noise-limited gate fidelities.
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Abstract Spin qubits in semiconductor quantum dots offer a gate-tunable platform for quantum information processing. While two-qubit interactions are typically realized through exchange coupling between neighboring spins, coupling spin qubits to photons via hybrid spin-circuit QED (cQED) devices enables long-range interactions and integration with other cQED platforms. Here, we investigate hole spin–photon coupling in compact single quantum dot setups. By incorporating ubiquitous strain inhomogeneities to our theory, we identify three main spin–photon coupling channels: a vector-potential-spin–orbit geometric mechanism–dominant for vertical magnetic fields–, an inhomogeneous Rashba term generalizing previous spin–orbit field models, and strain-induced g -tensor terms–most relevant for in-plane fields. Comparing Si, unstrained (relaxed) Ge, and biaxially strained Ge wells, we find that Si and unstrained Ge provide optimal coupling strengths (tens of MHz) thanks to their reduced heavy-hole, light-hole splitting. We demonstrate efficient switching of the spin–photon coupling while preserving sweet spot conditions by operating with an in-plane magnetic field. Finally, we evaluate quantum state transfer and two-qubit gate protocols, achieving ≳ 99 % fidelity for state transfer and > 90 % for two-qubit gates with realistic coherence times, establishing single-dot hole spins as a viable platform for compact spin-cQED architectures and highlighting unstrained Ge as a promising candidate for spin–photon interactions.