A tunable Purcell filter design for multiplexed qubit readout

High fidelity and multiplexed qubit readout is a key ingredient to the realization of a quantum processor. One factor limiting the readout fidelity of a superconducting qubit is photon leakage into the readout line which reduces the qubit lifetime ($T_1$). To prevent this effect, Purcell filters can be used to suppress readout line modes at the qubit frequency, while keeping maximal transmission at the readout frequency.

In this work, we present a filter design allowing multiplexed qubit readout with Purcell protection. The design is composed of four quarter-wave stubs, providing a bandstop filter whose bandwidth is up to 1~GHz at the qubit frequency. Using a three-port scattering matrix formalism, we show that the qubit emission into the readout line is suppressed by more than 75~dB, while the readout line transmission is reduced by less than 3~dB. We then show that in situ tunability of the filter can be obtained by terminating the stubs with RF-Squids. Our results pave the way to large-scale qubit readout with high fidelity and flexibility.