Kinetic inductance coupling for circuit QED with spins

While transverse coupling ( {σ}_x ) is commonly used in qubit-resonator systems, longitudinal coupling via {σ}_z presents a tantalizing alternative: it does not hybridize the modes, eliminating Purcell decay, and it enables quantum-nondemolition qubit readout independent of the qubit-resonator frequency detuning. Here, we demonstrate longitudinal coupling between a {{Cr}₇Ni} molecular spin qubit ensemble and the kinetic inductance of a granular aluminum superconducting microwave resonator. The inherent frequency independence of this coupling allows for the utilization of a 7.8-GHz readout resonator to measure the full {{Cr}₇Ni} magnetization curve spanning 0–600 mT, corresponding to a spin frequency range of {f}_spin=0 –15 GHz. For 2-GHz detuning from the readout resonator, we measure a 1/e spin relaxation time of τ=0.38 s, limited by phonon decay to the substrate. Based on these results, we propose a path towards longitudinal coupling of single spins to a superconducting fluxonium qubit.