Validity of resonant two-qubit gates in the ultrastrong coupling regime of circuit quantum electrodynamics

We investigate theoretically the performance of resonant two-qubit gates in the crossover from the strong to the ultrastrong coupling regime of light-matter interaction in circuit quantum electrodynamics. Two controlled-phase (CPHASE) gate schemes—which work well within the rotating wave-approximation—are analysed while taking into account the effects of counter-rotating terms appearing in the Hamiltonian. Our numerical results show that the fidelity of the gate operation is above 96% when the ratio between the coupling strength and the resonator frequency, g/ωr, is about 10%. Novel schemes are required in order to implement ultrafast quantum gates when increasing the ratio g/ωr. (paper)