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arXiv:2601.01704

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, S. Bhattarai, A. Prem

cond-mat.mes-hallphysics.app-phquant-phSubmitted Jan 5, 2026• Announced Jan 6, 2026
v1 · Jan 5, 2026v2 · May 6, 2026
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Abstract

We present a device-level design for a two-qubit module based on phonon-coupled germanium (Ge) hole-spin qubits operating at $1$-$4~\mathrm{K}$. Building on prior work on phonon-engineered Ge qubits and phononic-crystal (PnC) cavities, we specify a lithography-ready layout that integrates two gate-defined hole-spin qubits in a strained Ge quantum well with a GHz PnC defect mode that mediates a coherent phonon-based interaction. We detail the SiGe/Ge heterostructure, PnC cavity design, and a compatible nanofabrication process flow, including the gate stack, membrane patterning and release, and RF/DC wiring. We further develop a readout architecture combining spin-to-charge conversion with RF reflectometry on a proximal charge sensor, supported by a cryogenic RF chain optimized for operation at $1$-$4~\mathrm{K}$. Finally, we outline the cryogenic measurement environment, tuning procedures, and a stepwise benchmarking program targeting single-qubit control, phonon-bandgap suppression of relaxation channels, and resolvable phonon-mediated two-qubit coupling. The resulting module provides a scalable template for medium-range coupling of Ge hole-spin qubits and connects materials and phonon engineering with circuit-level readout, enabling future experimental demonstrations of entangling gates, Bell-state generation, and phonon-enabled quantum sensing.

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16 pages, 7 figures, and 1 table

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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.
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.
Germanium hole spin qubits based on strained Ge/SiGe quantum well have attracted much research attention due to the strong spin-orbit coupling. In particular, the strain dependence of the heavy-hole--light-hole mixing and thus the ggg-tensor anisotropy offer unique opportunities for acoustic driving and spin-phonon coupling. In this work we numerically simulate the coherent control of a Ge hole spin using surface acoustic waves. The periodic strain dynamically modulates the ggg-tensor matrix and causes fast spin rotation under a small acoustic amplitude. Moreover, we show a strong anisotropy and confinement dependence of the Rabi frequency coming from the phase-shifted longitudinal and shear strain components. Our work lays the foundations for acoustic-driven spin control and spin-phonon coupling using Ge hole spin qubits.