Hole spin qubits provide one of the leading platforms for spin-based quantum computing due to their large intrinsic spin-orbit interaction (SOI), which enables fast electrical manipulation. The SOI of planar quantum dots has mostly been investigated in theoretical studies by examining the SOI already present in the two-dimensional hole gas (2DHG). Here, we study the SOI created by the in-plane confinement by deriving non-perturbative effective Hamiltonians numerically for hole spin qubits. We find that the quantum geometry of the 2DHG naturally emerges, leading to a meaningful non-perturbative definition of pseudospin valid far away from the $Γ$-point. The SOI of the 2DHG and of the in-plane confinement have different forms; therefore, they cannot be turned off simultaneously, ruining the perfect spin-orbit switch functionality of spin qubits. We construct effective Hamiltonians using the symmetry approach for various low-dimensional hole systems: (i) a heavy-hole confined in a SiGe/Ge/SiGe heterostructure, (ii) a light-hole confined in SnGe/Ge, (iii) a gate-defined nanowire in SiGe/Ge/SiGe, and (iv) a hole confined in a Ge/Si core/shell nanowire. The non-perturbative effective Hamiltonians provide results with excellent agreement with the full Hamiltonians.
Hole spin qubits provide one of the leading platforms for spin-based quantum computing due to their large intrinsic spin-orbit interaction (SOI), which enables fast electrical manipulation. The SOI of planar quantum dots has mostly been investigated in theoretical studies by examining the SOI already present in the two-dimensional hole gas (2DHG). Here, we study the SOI created by the in-plane confinement by deriving non-perturbative effective Hamiltonians numerically for hole spin qubits. We find that the quantum geometry of the 2DHG naturally emerges, leading to a meaningful non-perturbative definition of pseudospin valid far away from the Γ-point. The SOI of the 2DHG and of the in-plane confinement have different forms; therefore, they cannot be turned off simultaneously, ruining the perfect spin-orbit switch functionality of spin qubits. We construct effective Hamiltonians using the symmetry approach for various low-dimensional hole systems: (i) a heavy-hole confined in a SiGe/Ge/SiGe heterostructure, (ii) a light-hole confined in SnGe/Ge, (iii) a gate-defined nanowire in SiGe/Ge/SiGe, and (iv) a hole confined in a Ge/Si core/shell nanowire. The non-perturbative effective Hamiltonians provide results with excellent agreement with the full Hamiltonians.
Compressively strained Ge quantum wells in planar SiGe/Ge heterostructures are the state-of-the-art platform for hole spin qubits. While they exhibit robust coherence times, they possess weak intrinsic spin-orbit interaction (SOI) due to the heavy-hole (HH) character of the wavefunction. Recently, light-hole (LH) qubits were proposed in GeSn/Ge heterostructures, offering strong, intrinsic, linear-in-momentum SOI. In this work, we propose a switchable HH-LH spin qubit in a bilayer Ge heterostructure with SiGeSn barriers, combining the advantages of HH and LH devices. The character of the qubit can be changed by shuttling from an LH well to an HH well, which also enables fast, hopping-based single-qubit rotations. Additionally, we observe an HH-LH resonance introduced by the in-plane confinement, resulting in g-factor peaks and first-order charge noise sweet spots. Our calculations reveal a sweet spot with Rabi frequencies on the order of 100 MHz, comparable to the LH regime, but with a more than tenfold increase in coherence time, on the order of 100 μs.
Disentangling orbital and confinement contributions to g-factor in Ge/SiGe hole quantum dots
Spin qubits are typically operated in the lowest orbital of a quantum dot to minimize interference from nearby states. In valence-band hole systems, strong spin-orbit coupling links spin and orbital degrees of freedom, strongly influencing the hole g-factor, a key parameter for qubit control. We investigate the out-of-plane g-factor in Ge quantum dots using excitation (single-particle) and addition (many-body) spectra. Excitation spectra allow us to distinguish the pure Zeeman g-factor from orbital contributions to the magnetic field splitting of states despite the strong spin-orbit coupling. This distinction clarifies discrepancies between g-factors extracted with the two methods, for different orbital states and different hole numbers. Furthermore, we find gate-tunability of g-factors at the level of 15%, highlighting its relevance for all-electric qubit manipulation.
The selective confinement of light holes (LHs) is demonstrated by introducing a low-dimensional system consisting of a highly tensile-strained Ge quantum well enabling the design of an ultrafast gate-defined spin qubit under the electric dipole spin resonance. The qubit size-dependent g factor and dipole moment are mapped, and the parameters inducing their modulation are discussed. It is found that the LH qubit dipole moment is two to three orders of magnitude higher than that of the canonical heavy-hole qubit. This behavior originates from the significant spin splitting resulting from the combined action of large cubic and linear Rashba spin-orbit interactions that are peculiar to LHs. The qubit relaxation rate is also affected by the strong spin-orbit interaction and follows typically a B7 behavior. The proposed all-group IV, direct band-gap LH qubit provides an effective platform for a scalable qubit-optical photon interface sought after for long-range entanglement distribution and quantum networks.
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.
Planar germanium heterostructures hosting hole-spin qubits are among the leading platforms for scalable semiconductor-based quantum computing. Yet, device performance is hindered by significant quantum dot variability, which leads to uncertainty in qubit energy levels and random orientations of the spin quantization axis. Tailored control of the g-tensor offers a strategy to overcome these limitations and achieve more reliable qubit operations. Here, we introduce a flexible optimization framework for engineering g-tensor properties. As a benchmark, we numerically obtain the optimal reshaping of the out-of-plane potential in a SiGe-Ge-SiGe quantum well to suppress the in-plane g-tensor components and realize the recently proposed gapless single-spin qubit encoding. This reshaping is achieved through heterostructure engineering, specifically by adjusting the silicon concentration within the quantum well, though the framework remains readily adaptable to alternative design objectives. Our results provide practical design principles for improving the tunability of the spin response, paving the way towards large-scale germanium-based quantum computers.
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 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 g 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.