Longitudinal (curvature) couplings of an N -level qudit to a superconducting resonator at the adiabatic limit and beyond

Understanding the coupling of superconducting (SC) wires to solid state qubits is vital to the design of quantum computers. To date, there has not been a complete theory applicable to all parameter regimes, from the traditional dispersive regime of circuit QED to the resonance regime to the far-off resonance situation in the adiabatic regime. This work presents that theory in the context of modulated longitudinal coupling, which promises to enhance the readout and coupling speed and fidelity through a resonator of solid-state qubit operations.