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

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.