A Compact Broadband Purcell Filter for Superconducting Quantum Circuits in a 3D Flip-Chip Architecture

Abstract

Fast and high-fidelity qubit readout requires strong coupling between the readout resonator and the feedline. However, such coupling unavoidably enhances qubit decay through the Purcell effect. We present a four-pole broadband Purcell filter implemented on a 3D flip-chip platform to overcome this trade-off. The filter provides a flat 1 GHz passband centered at 7.68 GHz and achieves more than 45 dB suppression at typical qubit frequencies. We demonstrate the filter's compatibility with multiplexed readout using a test chip that integrates six floating readout resonators strongly coupled within the passband. The chip is fabricated using a 150 nm Niobium (Nb) thin-film process and characterized at 20 mK in a cryogenic measurement setup. We also develop an analytical model that accurately captures the filter response and determines the resonance frequencies and external quality factors of the floating resonators directly from their physical geometry, enabling rapid circuit synthesis and design optimization. The proposed design is compact and fabrication-tolerant, making it a practical solution for large-scale superconducting quantum processors.

Figures (11)

• Figure 1: (a) Cross-sectional view at AA' plane in (f) (not to scale), illustrating the chip stack-up and the coupling section between readout resonator and Purcell filter. The BB' plane denotes the symmetry plane used for conformal mapping analysis. (b) False-colored micrograph of the fabricated sample showing the top and bottom chips in an overlapped configuration. (c) Isometric view of the 3D model, unveiling the top chip to show both the metal layers facing each other. The indium bumps are only shown on bottom chip for better visibility. The feedline and spiral resonators are implemented on the bottom chip, while the coplanar waveguide (CPW) line resonator and meandering readout resonators are patterned on the top chip. (d) Coupling section between two CPW line resonators of the Purcell filter. (e) Parallel-plate capacitance between the spiral and CPW line resonators enabling over-the-air coupling. (f) Floating readout resonator coupled to the CPW line resonator within the filter passband. (g) Spiral resonator and tapped-in feedline providing external coupling.
• Figure 2: (a) Schematic of the chip and the coupling scheme between resonators along the signal path. (b) Coupling topology of the four-pole Purcell filter and the configuration of the in-band coupled readout resonators.
• Figure 3: General distributed-element model of two coupled $\lambda/4$ resonators, with short- and open-circuit boundary conditions applied to the respective ports.
• Figure 4: Extracted coupling coefficients of two coupled $\lambda/4$ resonators with different geometric parameters, obtained from the proposed analytical model (solid lines) and Ansys HFSS eigenmode simulations (dash lines).
• Figure 5: Extracted coupling coefficients $M_{12}$ between spiral and CPW line resonator, and the corresponding bare frequency of the CPW line resonator, obtained from Ansys HFSS eigenmode simulations. The patch size of the CPW line resonator $w_{p}^{\text{line}}$ is swept, while the patch size of the spiral resonator is fixed at $w_{p}^{\text{spiral}} = 110\,\mu\text{m}$.