Perfect displacement of a superconducting resonator via fast-forward scaling and its application to high-speed $R_{ZZ}$ gates in Kerr-cat qubits

We investigate the fast-forward and time-scaling properties of superconducting resonators under an off-resonant coherent drive. We propose a scheme for perfect displacement of a superconducting resonator by modulating the drive amplitude based on fast-forward scaling theory. Furthermore, we propose a scheme exploiting both the fast-forward and time-scaling properties that enables perfect displacement through detuning modulation. The proposed schemes are also applicable to a subsystem that can be effectively represented by a driven resonator. In particular, we apply the latter scheme to fast and high-fidelity displacement of a coupler between Kerr parametric oscillators, which leads to high-speed $R_{ZZ}$ gates in Kerr-cat qubits.