Josephson Junction-Based Compact Notch Purcell Filters for Superconducting Qubit Readout

High-fidelity qubit readout in circuit QED requires suppressing relaxation due to the Purcell effect, typically achieved through the use of Purcell filters. A key limitation of existing Purcell filter implementations is their large footprint. In this work, we propose a compact notch Purcell filter based on a Josephson junction (JJ) chain embedded in series with the readout resonator. We analytically derive the conditions for operation in the dispersive regime using a lumped-element model, and validate the concept through an example design that is analyzed through both lumped-element and full electromagnetic simulations. The results indicate that the proposed architecture achieves a Purcell decay time exceeding 1 ms, with a dispersive shift and resonator linewidth of approximately 10 MHz, enabling fast, high signal-tonoise ratio readout. As typical of notch filters, also this solution exhibits an inherent parameter sensitivity. SQUIDs can be used for post-fabrication frequency tuning, at the expense of an increase of the number of required control lines.