Saturable Purcell filter for circuit QED

We consider a typical circuit QED setup where a data artificial atom encodes a qubit and is dispersively coupled to a measurement resonator that in turn is coupled to a transmission line. We show theoretically that by placing a filter artificial atom in this transmission line, the effective decay of the data artificial atom into the transmission line (the Purcell decay) is suppressed. When strong control fields are present in the transmission line, the filter artificial atom is saturated and hence effectively switched off. This permits both control and measurement of the data artificial atom using a single transmission line, while maintaining the Purcell filtering capability and therefore a long coherence time of the data artificial atom in the absence of the control pulses. We also apply open systems optimal control techniques to optimize the π-pulse on the data artificial atom, achieving high fidelity. The considered setup is compatible with the frequency multiplexing, potentially enabling both control and measurement of several qubits using a single Purcell-filtered transmission line. Our work helps with the scalability of the superconducting quantum computers by decreasing the ratio between the number of qubits and the number of the required transmission lines. For the setups that already use one transmission line both for measurement and control, our work provides a way to add Purcell filtering without removing the possibility of controlling the system.