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

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.