Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2606.22067

Detector-Grade Germanium as a Low-Disorder Host for Indium-Acceptor Spin Qubits: A Five-Qubit Materials-to-Architecture Design Study

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

quant-phSubmitted Jun 20, 2026• Announced Jun 23, 2026
arXivHTMLPDF

Abstract

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 $10^{10} \mathrm{cm^{-3}}$ with a target In density of approximately $2\times10^{14} \mathrm{cm^{-3}}$, corresponding to an acceptor spacing of about 170 nanometer. A 1 $μ$m-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.

Comments
45 pages, 4 figures, 7 tables

Related papers

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 +4 more

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.

quant-pharXiv:2605.13680•May 14, 2026

Two-Qubit Module Based on Phonon-Coupled Ge Hole-Spin Qubits: Design, Fabrication, and Readout at 1-4 K

D. -M. Mei, S. A. Panamaldeniya, K. -M. Dong +2 more

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 $1$--$4~\mathrm{K}$. 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.

cond-mat.mes-hallCross-listedarXiv:2601.01704•Jan 6, 2026

Enhancing charge stability of Ge quantum well heterostructures via SiGe layer composition engineering

Ding-Ming Huang, Jun-Hang Liu, Han Gao +10 more

Composition modulation is a powerful technique for designing materials with tailored properties, fueling the development of advanced semiconductor devices. In this work, we have implemented this technique into Ge quantum well heterostructures, offering a promising avenue to address the critical challenge of charge stability in spin qubit devices. Harnessing the atomic-scale precision of molecular beam epitaxy, we have engineered the band structure of the SiGe top barrier via graded composition modulation, thereby reducing charge accumulation states at the SiGe-dielectric interface and strengthening the effective confinement to the hole gases in the Ge quantum wells. The enhanced charge stability of composition-modulated SiGe/Ge quantum well heterostructures is confirmed in Hall devices, featuring an enlarged stable gate voltage range. We have further fabricated quantum dot devices from the composition-modulated SiGe/Ge quantum well heterostructures and observed remarkably low charge noise with an averaged amplitude of $0.46\,\mathrm{μeV}/\mathrm{\sqrt{Hz}}$ at $1\,\mathrm{Hz}$---the lowest reported value for Ge quantum wells grown on silicon. This exceptional charge stability of the quantum dots persists in the few-hole regime, with no observable voltage drift over $\sim$hours. With reduced charge noise and enhanced energy stability, composition-modulated SiGe/Ge heterostructures exhibit significant potential for applications in building high-performance quantum devices, including spin qubits with a long coherence time.

cond-mat.mes-hallCross-listedarXiv:2609.11214•Sep 11, 2026

Circuit Quantum Electrodynamics and Spin Qubits with Multi-Hole Quantum Dots in planar Germanium

Franco De Palma

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.

•Jan 1, 2026•0 citations

Electrically Tuneable Variability in Germanium Hole Spin Qubits

Edmondo Valvo, Michele Jakob, Patrick Del Vecchio +2 more

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.

cond-mat.mes-hallCross-listedarXiv:2512.12702•Dec 16, 2025

Strain engineering of Andreev spin qubits in Germanium

Vittorio Coppini, Patrick Del Vecchio, Antonio L. R. Manesco +4 more

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.

arXiv:2604.22650•Apr 24, 2026•0 citations
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.
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 LLL-point conduction band, the spin-3/23/23/2 valence band, heavy-hole/light-hole mixing, strain, interfaces, disorder, and phonons. We also introduce a common framework for estimating phononic-crystal-modified T1T_1T1​ 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.
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.
Composition modulation is a powerful technique for designing materials with tailored properties, fueling the development of advanced semiconductor devices. In this work, we have implemented this technique into Ge quantum well heterostructures, offering a promising avenue to address the critical challenge of charge stability in spin qubit devices. Harnessing the atomic-scale precision of molecular beam epitaxy, we have engineered the band structure of the SiGe top barrier via graded composition modulation, thereby reducing charge accumulation states at the SiGe-dielectric interface and strengthening the effective confinement to the hole gases in the Ge quantum wells. The enhanced charge stability of composition-modulated SiGe/Ge quantum well heterostructures is confirmed in Hall devices, featuring an enlarged stable gate voltage range. We have further fabricated quantum dot devices from the composition-modulated SiGe/Ge quantum well heterostructures and observed remarkably low charge noise with an averaged amplitude of 0.46 μeV/Hz0.46\,\mathrm{μeV}/\mathrm{\sqrt{Hz}}0.46μeV/Hz​ at 1 Hz1\,\mathrm{Hz}1Hz---the lowest reported value for Ge quantum wells grown on silicon. This exceptional charge stability of the quantum dots persists in the few-hole regime, with no observable voltage drift over ∼\sim∼hours. With reduced charge noise and enhanced energy stability, composition-modulated SiGe/Ge heterostructures exhibit significant potential for applications in building high-performance quantum devices, including spin qubits with a long coherence time.
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.
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 ggg-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.
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.