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arXiv:2605.13680

Comparative assessment of germanium-based spin-qubit modalities: donor, acceptor, gate-defined hole, and gate-defined electron platforms

D. -M. Mei, K. -M. Dong, S. A. Panamaldeniya, A. Prem, S. Chhetri, N. Budhathoki, S. Bhattarai

quant-phSubmitted May 13, 2026• Announced May 14, 2026• Revised Aug 14, 2026 (v4)
v1 · May 13, 2026v2 · Jul 19, 2026v3 · Jul 31, 2026v4 · Aug 14, 2026
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Abstract

High-purity germanium (Ge) has re-emerged as a versatile semiconductor platform for spin-based quantum information processing because it combines mature materials processing, access to spin-free isotopes, high mobilities, small effective masses, and strong but engineerable spin--orbit coupling. However, ``Ge qubits'' are not a single technology. Donor spin qubits, acceptor spin qubits, gate-defined hole spin qubits, and gate-defined electron spin qubits exploit different parts of the Ge band structure and therefore make distinct trade-offs among coherence, controllability, fabrication complexity, and scalability. Here we compare these four Ge-based spin-qubit modalities on a common physical and architectural footing. We review the shared Ge materials physics, including isotopic purification, the multivalley \(L\)-point conduction band, the spin-\(3/2\) valence band, heavy-hole/light-hole mixing, strain, interfaces, disorder, and phonons. We also introduce a common framework for estimating phononic-crystal-modified \(T_1\) using a calibrated reference relaxation rate, a geometry-dependent strain-density-of-states suppression factor, and parasitic relaxation channels. The comparison shows that gate-defined Ge hole-spin qubits currently offer the strongest combination of all-electrical control, demonstrated multiqubit operation, and scalability. Donor, acceptor, and gate-defined electron qubits remain important complementary directions for memory, hybrid, and exploratory architectures. Overall, Ge supports a diverse qubit ecosystem, with gate-defined hole-spin qubits presently providing the clearest path toward scalable Ge-based quantum processors.

Comments
44 pages, 5 figures, and 7 tables

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High-purity germanium (Ge) has re-emerged as a versatile semiconductor platform for spin-based quantum information processing because it combines mature materials processing, access to spin-free isotopes, high mobilities, small effective masses, and strong but engineerable spin--orbit coupling. However, ``Ge qubits'' are not a single technology. Donor spin qubits, acceptor spin qubits, gate-defined hole spin qubits, and gate-defined electron spin qubits exploit different parts of the Ge band structure and therefore make distinct trade-offs among coherence, controllability, fabrication complexity, and scalability. Here we compare these four Ge-based spin-qubit modalities on a common physical and architectural footing. We review the shared Ge materials physics, including isotopic purification, the multivalley (L)-point conduction band, the spin-(3/2) valence band, heavy-hole/light-hole mixing, strain, interfaces, disorder, and phonons. We also introduce a common framework for estimating phononic-crystal-modified (T_1) using a calibrated reference relaxation rate, a geometry-dependent strain-density-of-states suppression factor, and parasitic relaxation channels. The comparison shows that gate-defined Ge hole-spin qubits currently offer the strongest combination of all-electrical control, demonstrated multiqubit operation, and scalability. Donor, acceptor, and gate-defined electron qubits remain important complementary directions for memory, hybrid, and exploratory architectures. Overall, Ge supports a diverse qubit ecosystem, with gate-defined hole-spin qubits presently providing the clearest path toward scalable Ge-based quantum processors.
Acceptor-bound hole spins in germanium (Ge) offer a promising but underexplored route to semiconductor quantum information processing. We present a theory-guided design study of a detector-grade Ge acceptor-spin platform based on intentionally incorporated indium (In) acceptors in ultra-high-purity Ge. The proposed materials strategy combines a residual impurity background near 1010cm−310^{10} \mathrm{cm^{-3}}1010cm−3 with a target In density of approximately 2×1014cm−32\times10^{14} \mathrm{cm^{-3}}2×1014cm−3, corresponding to an acceptor spacing of about 170 nanometer. A 1 μμμm-long active channel with a suitable transverse mode volume can contain about five acceptors on average, enabling a statistically selected post-fabrication register rather than a deterministically placed chain. We analyze the physical basis, device architecture, strain and disorder limits, coupling hierarchy, modeling workflow, fabrication pathway, and scaling prospects. Our results indicate that detector-grade Ge can suppress uncontrolled bulk electrostatic and strain disorder to levels compatible with acceptor-hole qubits, while the spin--orbit-active valence-band manifold supports all-electrical control and dipolar or phonon-mediated coupling. Direct exchange is treated as a close-pair or gate-enhanced interaction rather than the generic mean-spacing coupling. Phononic crystal engineering is identified as a second-stage enhancement for suppressing unwanted acoustic modes and enabling selected cavity-mediated interactions after baseline control, readout, and nearest-neighbor coupling are validated. Remaining challenges include statistical acceptor placement, interface disorder, charge noise, readout integration, and experimental validation. This work identifies detector-grade Ge In-acceptor qubits as a credible intermediate architecture between donor-based impurity qubits and fully gate-defined Ge hole-spin hardware.
The understanding of quantum mechanics enabled the development of technology such as transistors and has been the foundation of today’s information age. Actively using quantum mechanics to build quantum technology may cause a second revolution in handling information. However, to execute meaningful algorithms, largescale quantum computers have to be built. Such systems are constructed from many qubits, the quantum version of the classical bit. While exciting progress is being made across a range of different qubit platforms, achieving the radical scalability that is necessary to build a largescale processor could be a roadblock. Huge challenges are put on reproducibility, inand output connectivity and material quality. Qubits based on the spins of electrons and holes confined in semiconductor quantum dots may have an important advantage in constructing quantum processors. This platform can profit from the advanced semiconductor industry that was responsible for the first computing revolution. Group IV semiconductors such as silicon and germanium have a high compatibility with industrial semiconductor manufacturing and contain stable isotopes with zero nuclear spin. The materials can be isotopically purified and serve as excellent hosts for spins with long quantum coherence. In Chapter 3 we present quantum dot arrays in silicon metaloxidesemiconductor (SiMOS), strained silicon (Si/SiGe) and strained germanium (Ge/SiGe). A nearly identical integration scheme based on an overlapping gate structure can be used to define quantum dots in each platform. Each platform has its own opportunities, which are carefully assessed. By employing charge sensing we confirm that all quantum dots can be depleted to the singleelectron regime. We compare capacitive crosstalk and find it to be the smallest in SiMOS, relevant for the tuning of quantum dot arrays. Using this crossplatform integration, we can study qubits in each platform with minimal overhead. Long coherence times, excellent singlequbit gate fidelities and twoqubit logic have been demonstrated with SiMOS spin qubits, making it one of the leading platforms for quantum information processing. However, due to the high disorder at the Si/SiO2 interface compared to Ge/SiGe and Si/SiGe interface, quantum dots defined in SiMOS are small and achieving sufficient control over single electrons has been a long standing challenge. In Chapter 5 we show experiments on a double quantum dot that can be isolated from its reservoir. We demonstrate a tunable tunnel coupling between single electrons up to 13 GHz and tunable tunnel rates down to below 1 Hz. These results mark an important step towards the required degree of control over the location of and coupling between quantum dots, necessary for the operation of a large array.
We present a device-level design study for a two-qubit module based on phonon-coupled germanium (Ge) hole-spin qubits targeted for operation at 111--4 K4~\mathrm{K}4 K. Building on prior theoretical modeling of phonon-engineered Ge qubits and phononic-crystal (PnC) cavities, we translate those modeling results into a fabrication-oriented two-qubit layout that integrates two gate-defined hole-spin qubits in a strained Ge quantum well with a GHz PnC defect mode intended to mediate a coherent phonon-based interaction. We specify the SiGe/Ge heterostructure, electrostatic gate layout, PnC cavity geometry, and a compatible nanofabrication pathway, including gate-stack formation, membrane patterning and release, RF/DC wiring, and process-risk mitigation. We further develop a readout architecture combining spin-to-charge conversion with RF reflectometry on a proximal charge sensor, and we provide a link-budget estimate that states the assumed system noise temperature, RF signal contrast, and integration-time requirements for single-shot readout at elevated cryogenic temperatures. Finally, we outline a stepwise benchmarking program for charge stability, single-qubit control, phonon-bandgap modification of relaxation, and resolvable phonon-mediated two-qubit coupling. The manuscript does not report experimental device data; rather, it provides an experimentally actionable bridge from prior modeling to future fabrication and measurement of phonon-coupled Ge hole-spin modules.
Spin qubits have emerged as a leading platform for quantum information processing due to their long coherence times, small footprint, and compatibility with the existing semiconductor industry. We first provide an introduction to the different qubit implementations currently being investigated, including single electron-spin qubits, hole-spin qubits, donor qubits, and multispin encodings. We discuss how the confinement and strain present in semiconductor heterostructures produce addressable levels whose spin degree of freedom can be used to encode a qubit. A large emphasis is placed on reviewing the theoretical foundations and recent experimental demonstrations of proposed mechanisms for long-range coupling, including hybrid approaches based on circuit QED and Andreev qubits, as well as spin shuttling. Finally, we review a recent proposal for linking spin qubits using topological spin textures.
Strained germanium (ε\varepsilonε-Ge) quantum wells on metamorphic SiGe buffers have enabled advanced hole-based spin qubit devices. Alternatively, unstrained Ge with lattice-matched strained silicon-germanium (ε\varepsilonε-SiGe) barriers eliminates the need for metamorphic buffers altogether. The ground state character of both these platforms is predominantly heavy-hole (HH) with a largely anisotropic spin response. We propose and study an alternative heterostructure, lattice-matched to Ge, in which both the SiGe quantum well and barriers are tensile strained, with their composition contrast providing the band offset for confinement and the tensile strain stabilizing a light-hole (LH) ground state. We show large spin-orbit coupling (SOC), both linear and cubic, along with a significantly more isotropic spin response compared to strained HH qubits. We also study the decoherence properties of the proposed device, showing an appreciable gain in the quality factor compared to their HH counterparts. Finally, we propose a bilayer heterostructure that allows for electrical switching between HH and LH ground state character.
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.