Efficient numerical approach for the simulations of high-power dispersive readout with time-dependent unitary transformation

We develop an efficient numerical approach for simulating the high-power dispersive readout in circuit quantum electrodynamics. In the numerical simulations of the high-power readout, a large-amplitude coherent state induced in a cavity is an obstacle because many Fock states are required to describe such a state. We remove the large-amplitude coherent state from the numerical simulations by simulating the dynamics in a frame where the amplitude of the coherent state is almost absent. Using the developed method, we numerically simulate the high-power dispersive readout of the two-level system and the transmon. Our proposed method succeeds in producing reasonable behaviors of the high-power dispersive readout which can be deduced from the photon-number dependence of the cavity frequency: The high-power dispersive readout works in the two-level-system case while it does not work in the transmon case.