Proposed Three-Hole Quadrupole Qubit

Charge quadrupole qubits eliminate dipolar coupling to charge noise, offering enhanced coherence compared to conventional charge qubits. We adapt the recently proposed p-orbital (pO) qubit [Caporaletti et al., Phys. Rev. Lett. 135, 070803 (2025)], originally based on electrons in Si, to holes in Ge quantum dots, where strong spin-orbit coupling enables fast all-electrical control. Using a 4×4 Luttinger–Kohn model including heavy- and light-hole mixing, we construct the orbital manifold and derive an effective qubit Hamiltonian for a three-hole system within the frozen-core approximation. We study gate operations, driven by controlled anisotropy and quadrupole–quadrupole coupling, and estimate decoherence using an interface-dipole noise model adapted for Ge/SiGe heterostructures. We analyze the effect of strong spin-orbit coupling and provide estimates of its influence on charge-noise sensitivity and Rabi rates. These results establish the hole-based pO qubit as a compact, potentially magnet-free platform for fast, electrically controlled quantum logic.