Broadband Purcell filter design for superconducting qubits

Superconducting qubits are typically measured via dispersively-coupled readout resonators. To achieve fast readout without compromising the qubit's relaxation time T₁, Purcell filters have been developed. Commonly used single-pole Purcell filters have limited bandwidth thus constraining the multiplexed readout capacity. In this work, we present a systematic way to design multi-stage broad bandpass Purcell filters by use of a classical filter synthesis technique. We show that broadband filters can be designed with either equally loaded input and output ports (symmetric filters), or weakly coupled input ports and strongly coupled output ports (asymmetric or singly terminated filters). We analyze the performance of these multi-stage filters and numerically verify that a 6-stage symmetric filter and a 4-stage asymmetric filter with 600 MHz bandwidth can enhance the qubit lifetime over 1000-fold compared to the absence of filters. This is a hundredfold improvement over the performance of a single-pole filter of identical bandwidth. We experimentally implement this approach and test a simple, robust design that only uses sections of transmission lines.