Breaking the trade-off between gate and relaxation times of a superconducting qubit with a Josephson quantum filter: Theory*

When we couple a superconducting qubit strongly to a transmission line, the qubit completely reflects a weak resonant microwave field propagating through the line. On the other hand, the qubit becomes transparent to a stronger field due to the absorption saturation. This implies that a superconducting qubit functions as a nonlinear mirror, which we call a Josephson quantum filter (JQF). We theoretically investigate a setup in which a qubit (data qubit) to be controlled is coupled to an end of a semi-infinite control line and a JQF is placed at a distance of the order of the resonance wavelength of the qubit. An effective cavity is formed by the termination point and the JQF, and the radiative decay of the data qubit is suppressed if this effective cavity has a large detuning from the data qubit. Nearly complete suppression is achieved under the following conditions: the radiative decay rate of JQF is much larger than that of the data qubit, and the distance between the data qubit and the JQF is close to the half of the resonance wavelength.