Unstrained bulk germanium is a particularly attractive material for circuit quantum electrodynamics with spins (spin-cQED). We show, through systematic modeling and comparison with state-of-the-art strained germanium heterostructures, that hole spins in bulk germanium double quantum dots readily reach the strong-coupling regime with superconducting microwave resonators, achieving spin-photon coupling strengths $g_s/2π\gtrsim100$\,MHz. This enhancement originates from large spin-orbit interactions beyond the perturbative regime. In addition, the coupling is much less sensitive to the orientation of the applied magnetic field, which shall ease operation and limit the impact of device-to-device variability. Our results establish bulk germanium as a compelling platform for scalable spin-cQED.
Unstrained bulk germanium is a particularly attractive material for circuit quantum electrodynamics with spins (spin-cQED). We show, through systematic modeling and comparison with state-of-the-art strained germanium heterostructures, that hole spins in bulk germanium double quantum dots readily reach the strong-coupling regime with superconducting microwave resonators, achieving spin-photon coupling strengths gs/2π≳100,MHz. This enhancement originates from large spin-orbit interactions beyond the perturbative regime. In addition, the coupling is much less sensitive to the orientation of the applied magnetic field, which shall ease operation and limit the impact of device-to-device variability. Our results establish bulk germanium as a compelling platform for scalable spin-cQED.
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.
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.
Planar germanium heterostructures are promising hosts for hybrid quantum devices due to their compatibility with superconductors, low material disorder, and relaxed fabrication constraints. Also, the potentially low density of nuclear spins and strong spin-orbit interaction make germanium attractive for coherent spin physics. However, recent microwave spectroscopy experiments were unable to resolve a spin-splitting of bound states in germanium Josephson junctions, the prerequisite for defining and controlling Andreev spin qubits. Here, we argue that compressive strain is the key mechanism suppressing spin splitting in current devices. Furthermore, we propose unstrained and tensile-strained heterostructures, fully compatible with state-of-the-art growth technology, that significantly enhance the relevant spin-orbit effect. By numerically simulating ballistic Josephson junctions, we predict spin splittings comfortably in the GHz range, more than 2 orders of magnitude larger than compressively strained cases, and all-electric quantum gates in a hundred nanoseconds. Our results establish strain engineering as a key design principle for realizing Andreev spin qubits in germanium-based devices.
Abstract The germanium (Ge) hut wire system has strong spin–orbit coupling, a long coherence time due to a very large heavy-light hole splitting, and the advantage of site-controlled large-scale hut wire positioning. These properties make the Ge hut wire a promising candidate for the realization of strong coupling of spin to superconducting resonators and scalability for multiple qubit coupling. We have coupled a reflection line resonator to a hole double quantum dot (DQD) formed in Ge hut wire. The amplitude and phase responses of the microwave resonator revealed that the charge stability diagrams of the DQD are in good agreement with those obtained from transport measurements. The DQD interdot tunneling rate is shown to be tunable from 6.2 GHz to 8.5 GHz, which demonstrates the ability to adjust the frequency detuning between the qubit and the resonator. Furthermore, we achieved a hole–resonator coupling strength of up to 15 MHz, with a charge qubit decoherence rate of 0.28 GHz. Meanwhile the hole spin–resonator coupling rate was estimated to be 3 MHz. These results suggest that holes of a DQD in a Ge hut wire are dipole coupled to microwave photons, potentially enabling tunable hole spin–photon interactions in Ge with an inherent spin–orbit coupling.
Hole spin qubits in planar germanium heterostructures are frontrunners for scalable semiconductor quantum computing. However, their current performance is mostly limited by large dot-to-dot variability that leads to uncontrolled qubit energies and random tilts in the spin quantization axis. Here, we propose a systematic and local method to engineer the spin qubit response by imprinting a controlled anisotropy in the quantum dot confinement, enabling on-demand electric g-tensor control. In particular, we find that both the quantum-dot size and asymmetry allow electrical tuning of the g-tensor and significantly suppress magnitude and angular variability of the spin response for selected magnetic field directions. We confirm this behavior by analyzing single-disorder realizations and statistical ensembles in state-of-the-art strained and unstrained germanium channels, showing that the latter provides an optimal path for g-tensor engineering. Our results provide practical design principles for on-demand control of the spin response and mitigating variability, paving the way towards large-scale germanium-based quantum computers.
Hole spin qubits are frontrunner platforms for scalable quantum computers because of their large spin-orbit interaction that enables ultrafast all-electric qubit control at low power. The fastest spin qubits to date are defined in long quantum dots with two tight confinement directions, when the driving field is aligned to the smooth direction. However, in these systems the lifetime of the qubit is strongly limited by charge noise, a major issue in hole qubits. We propose here a different, scalable qubit design, compatible with planar CMOS technology, where the hole is confined in a curved germanium quantum well surrounded by silicon. This design takes full advantage of the strong spin-orbit interaction of holes, and at the same time suppresses charge noise in a wide range of configurations, enabling highly coherent, ultrafast qubit gates. While here we focus on a Si/Ge/Si curved quantum well, our design is also applicable to different semiconductors. These devices allow for ultrafast operations even in short quantum dots by a transversal electric field. This additional driving mechanism relaxes the demanding design constraints, and offers a way to reliably interface spin qubits in a single quantum dot to microwave photons. By considering state-of-the-art high-impedance resonators and realistic qubit designs, we estimate interaction strengths of a few hundreds of megahertz, largely exceeding the decay rate of spins and photons. Reaching such a strong coupling regime in hole spin qubits will be a significant step towards high-fidelity entangling operations between distant qubits, as well as fast single-shot readout, and could pave the way towards the implementation of a large-scale semiconducting quantum processor.