The present disclosure relates, inter alia, to a non-linear superconducting
quantum circuit having a first mode and a second mode. The first mode and the second mode each have a corresponding resonant frequency. 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. Thus, the circuit inherently performs resonant 2N-to-1
photon switching between the first mode and the second mode, respectively, where N is a positive integer. This forms an improved non-linear superconducting
quantum circuit. The circuit may stabilize the cat qubits when the circuit receives a predetermined current and the second mode is properly driven. In order to perform
quantum measurements on the circuit, a method is proposed for performing quantum measurements by switching off the driving of the second mode to switch to a non-driving manifold.