Optimizing Signal to Noise Ratio for Superconducting Qubit Readout with a Purcell Filter*

Superconducting qubit readout remains one of the most important aspects to improve in circuit quantum electrodynamics, with the fidelity and length of the operation typically lagging in comparison to state-of-the-art single and two qubit gates. Purcell filters have been a significant advancement in this field, demonstrating to be vital in suppressing the resonator-induced qubit decay rate, known as the Purcell decay rate. However, the introduction of an additional mode increases the complexity of readout, with many parameters requiring simultaneous optimization. In this work, we explore calibration of the parameter space for the combined readout resonator-Purcell filter system to maximize the Signal-to-Noise ratio for readout given a finite readout time.