A non-linear superconducting
quantum circuit having a first mode and a second mode is disclosed, wherein the first and second
modes have respective resonant frequencies. The circuit is configured such that the resonant frequency of the second mode is substantially 2N times the resonant frequency of the first mode when a predetermined current of a
constant intensity is applied to the circuit. The circuit intrinsically performs a resonant 2N-to-1
photon exchange between the first and second
modes, with N being a positive integer, and thus improving the circuit. When this circuit receives a predetermined current and when the second mode is driven appropriately, the circuit can stabilize a cat-
qubit. In a symmetrical version of this circuit, a flux line has been developed to allow RF
coupling to the second mode and not to the first mode, allowing the stabilization to be turned off and
quantum measurements to be performed.