Fast readout at optimal point of a hopping Ge-hole spin qubit via dynamical longitudinal coupling to a superconducting resonator

Ge-hole quantum dot (QD) spin qubit based on recently proposed semiconductor hopping spins received attention due to simple one- and two- qubit operations in the presence of strong spin-orbit interactions in a low magnetic field [1]. By mapping its state to a state of auxiliary singlet-triplet qubit one performs a measurement of the latter via Pauli spin blockade (PSB) and a charge sensor [1,2]. This scheme has several drawbacks, including charge dephasing as well as a mismatch of states while passing to the spin blockade regime [2]. We study a possibility for a fast quantum readout of the intermediary singlet-triplet qubit via the dynamical longitudinal coupling in a dispersive regime [3]. Using an on-chip superconducting resonator for the readout the corresponding quantum measurement rate can be made much faster than the usual dispersive rate, allowing to overcome typical dephasing mechanisms. Readout optimization at various quantum dots’ detunings far from the PSB regime is further discussed.

[1] Chien-An Wang et al., Operating semiconductor quantum processors with hopping spins, Science 385, 447-452 (2024)

[2] E.G. Kelly et al., Identifying and mitigating errors in hole spin qubit readout, arXiv:2504.06898 (2025)

[3] R. Ruskov, C. Tahan, Longitudinal (curvature) couplings of an N-level qudit to a superconducting resonator at the adiabatic limit and beyond, Phys. Rev. B 109, 245303 (2024)