Figure 3. Time evolution of the fidelity F = |〈Ψ_S|Ψ_R〉|² of state |Ψ_S〉 evolving according to the digitized protocol, to the ideal state |Ψ_R〉 evolving according to the quantum Rabi dynamics, with a) , b) , c) , and d) .

The simulation is performed for different number n of Trotter steps. Black curves in the insets show the overlap of the ideal evolved state with the one at time t = 0, |〈Ψ_R|Ψ₀〉|², initialized with a fully excited qubit and the resonator in the vacuum state.