Figure 1. Frequency scheme of the stepwise implementation for the quantum Rabi Hamiltonian.

A transmon qubit of frequency ω_q is interacting with a microwave resonator, whose transition frequency is ω_r. The interactions H_1,2 in Eq. (3) are simulated respectively with a Jaynes-Cummings interaction (step 1), and another one with different detuning, anticipated and followed by π pulses (step 2).