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arXiv:2604.22650

Strain engineering of Andreev spin qubits in Germanium

Vittorio Coppini, Patrick Del Vecchio, Antonio L. R. Manesco, Anton Akhmerov, Valla Fatemi, Bernard van Heck, Stefano Bosco

Published Apr 24, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2604.22650

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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.
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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.
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≳100g_s/2π\gtrsim100gs​/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.
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.
We propose a variant of Andreev spin qubits (ASQs) defined in planar Josephson junctions based on spin-orbit coupled two-dimensional electron gases (2DEGs) in a weak out-of-plane magnetic field. The magnetic field induces a linear phase gradient across the junction, generating Josephson vortices that can host low-energy Andreev bound states (ABSs). We show that, in certain parameter regimes, the combined effect of the phase gradient and spin-orbit coupling stabilizes an odd-fermion parity ground state, where a single Josephson vortex binds a spinful low-energy degree of freedom that is energetically separated from the other ABSs. This low-energy degree of freedom can be exploited to define a special type of ASQ, which we dub the vortex spin qubit (VSQ). We show that single-qubit gates for VSQs can be performed via flux driving, while readout can be achieved by adapting standard circuit quantum electrodynamics (cQED) techniques developed for conventional ASQs. We further outline how an entangling two-qubit gate can be performed using an ac current drive. We argue that VSQs offer prospects for a substantial reduction in device complexity and hardware overhead compared to conventional ASQ implementations, while preserving key advantages such as supercurrent-based readout, single-qubit gates, and long-range two-qubit gates.
Andreev spin qubits (ASQs) are a promising platform for quantum information processing which benefit from both the small footprint of semiconducting spin qubits and the long range connectivity of superconducting qubits. While state-of-the-art experiments have developed ASQs in InAs nanowires, these realizations are coherence-time limited by nuclear magnetic noise which cannot be removed by isotopic purification. In Ge-based Josephson junctions, which can be isotopically purified, Andreev states have been experimentally observed but spin-resolved Andreev states remain elusive. Here, we theoretically demonstrate that the geometry of the Josephson junction can limit the qubit frequency to values below typical experimental temperatures and render the ASQ effectively invisible. ASQs could be experimentally resolved by judiciously choosing the geometry of the junction and filling of the underlying Ge. Our comprehensive study of ASQ frequency on in situ and ex situ experimentally controllable parameters provides design guidance of Ge-based Josephson junctions and paves the way towards realization of high-coherence ASQs.