Phonon-coupled hole-spin qubits in high-purity germanium: design and modeling of a scalable architecture

Abstract We present a design and modeling of a scalable quantum processor architecture utilizing hole-spin qubits defined in gate-controlled germanium (Ge) quantum dots, where coherent spin–phonon coupling is predicted to facilitate qubit manipulation and long-range interactions. The architecture exploits the strong, electrically tunable spin–orbit interactions intrinsic to hole states in Ge, integrated with high-quality phononic crystal cavities to enable fully electrical qubit control and phonon–mediated coupling. Employing a streamlined simulation framework built upon multiband <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:mi mathvariant="bold">k</mml:mi> </mml:mrow> <mml:mo>⋅</mml:mo> <mml:mrow> <mml:mi mathvariant="bold">p</mml:mi> </mml:mrow> </mml:mrow> </mml:math> modeling and finite-element methods, we quantify key performance metrics, including electrically tunable g -factors ranging from 1.3 to 2.0, spin–phonon coupling strengths up to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>6.3</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mrow> <mml:mi>MHz</mml:mi> </mml:mrow> </mml:mrow> </mml:math> , phononic cavity quality factors exceeding 10 4 , and phonon–mediated spin relaxation times ( T 1 ) reaching milliseconds. The proposed architecture concurrently achieves extended spin coherence and rapid gate operations through strategic electric field modulation and engineered phononic bandgap environments. Furthermore, isotopically enriched, high-purity Ge crystals significantly enhance device coherence by minimizing disorder and hyperfine interactions. This integrated approach, merging advanced materials engineering, precise spin–orbit coupling, and phononic cavity design, establishes a promising complementary metal–oxide–semiconductor-compatible pathway toward scalable, high-fidelity quantum computing.