Saturable Purcell filter for circuit QED

We consider a way to decrease the number of the transmission lines in the superconducting quantum computers by combining the separate lines used for control and measurement into one. While a combined control and measurement line can be used in the setup where an artificial atom is dispersively coupled to a resonator that in turn is attached to the line, this usually limits the coherence of the artificial atom due to the Purcell decay originating from a small effective coupling of the artificial atom to the line. Adding an unsaturable Purcell filter that suppresses frequencies close to the artificial atom transition and thereby the Purcell decay, makes the control of the artificial atom through the same line impossible, necessitating another line for control. We propose a saturable Purcell filter that consists of an artificial atom attached to the transmission line at a particular position. Such a Purcell filter is saturated and hence effectively turned off by the strong control pulses, and therefore a separate control transmission line is not needed. Our approach could be used together with the frequency multiplexing to further decrease the number of the required lines.