A non-linear superconducting
quantum circuit having a first mode and a second mode is disclosed, wherein the first mode and the second mode 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 respectively the first mode and the second mode, with N being a positive integer, thus improving the non-linear superconducting
quantum circuit. When this circuit receives a predetermined current and when the second mode is driven appropriately, the circuit can stabilize a cat-
qubit. In order to perform
quantum measurements on this circuit, the drive of the second mode is turned off, thus switching to a no-drive manifold such that the quantum measurements can be performed.