3D Integrated Embedded Filters for Superconducting Quantum Circuits

Abstract

Microwave filtering for superconducting qubits is a key element of quantum computing technology, enabling high coherence and fast state detection. This work presents the design and implementation of novel microwave Purcell filters for superconducting quantum circuits, integrated within a multilayer printed circuit board (PCB). The off-chip design removes all filter components from the qubit substrate, reducing device complexity, improving layout footprint and allowing better scalability to large qubit counts. Each embedded filter can couple up to nine readout resonators, enabling efficient multiplexed readout. Electromagnetic simulations of the filter predict a thousand-fold improvement in qubit isolation from the readout port. The design was experimentally validated under cryogenic conditions in conjunction with a 35-qubit device, demonstrating compatibility of the PCB-based filter with high-coherence superconducting qubits. The comparison of the measured qubit median T1 of 84 $μ$s with the expected radiative limit from electromagnetic simulations validated the presence of Purcell filtering in the system.

Figures (5)

• Figure 1: Processor readout stack. a. A diagram representing the components of a vertically-integrated QPU. This includes qubits $\textrm{Q}_1$ to $\textrm{Q}_\textrm{N}$ (blue), with individual control lines (with associated drive rates $\Omega_1$ to $\Omega_\textrm{N}$) and individually coupled readout resonators ($\textrm{R}_1$ to $\textrm{R}_\textrm{N}$, in green). The resonators interface with multiplexed bandpass filter(s) (B, in purple) whose coupling rate to the output line is denoted by $\kappa_\mathrm{ext}$. b. An illustration of the cross-sectional view of the physical layout of the readout stack (with no dedicated qubit control side); showing the qubit chip coupled to a unit cell of the PCB via an aluminum spacer.
• Figure 2: Embedded filter. a. Isometric top view of the building block 9--1 unit cell; showing the input vias, the embedded filter and the output port. Each filter is a triangular shape whose fundamental resonant mode determines the passband center frequency. Each filter capacitively couples to up to a maximum of nine readout resonators. A short-circuited stub in the center of the filter determines the filter bandwidth. b. Electric field profile from an eigenmode simulation of the embedded filter, corresponding to the mode at the fundamental frequency of the filter. This mode follows a drum-head behavior with a maximum field at the outside edges and a maximum current at the center. This enables a strong capacitive coupling to the readout resonators, while allowing a strong current coupling to a low impedance output port.
• Figure 3: Readout PCB. a. Photograph of the top (readout-resonator facing) layer of the readout PCB for at 35-qubit processor. The inset shows a zoomed version of the area within the dashed rectangle. Here one can see how the input vias (numbered 1 to 35) are arranged in a triangular grid, matching that of the qubits and readout resonators in the QPU. The embedded filters are tiled to enable full processor readout with six filters (highlighted within dashed lines and numbered R1 to R6 in the inset image). b. 3D rendering image of the physical QPU assembly, including the QPU itself, the embedded filter PCB, the readout wiring, and metallic sample holder parts. c. Blue scatter data (left vertical axis): readout resonator external quality factors, estimated from a full electromagnetic eigenmode simulation, including the PCB with embedded filter, nine resonators and nine qubits. Solid red line (right vertical axis): normalized quality factor inferred from a modal network simulation of the standalone PCB.
• Figure 4: Filter finite-element modeling. a. Quality factors of the qubit and the resonator modes, as a function of varying resonator frequency, extracted from eigenmode (blue scatter data, left vertical axis) and modal network (red lines, right vertical axis) finite-element simulations. b. Comparison of the qubit mode quality factors in a packaged QPU system with ($\blacktriangledown$ data and red dashed line) and without ($\bullet$ data and red solid line) embedded PCB filter.
• Figure 5: QPU metrics with embedded filters. a. Quality factor measurements of the readout resonators estimated from continuous-wave spectroscopy data. The external (red $\bullet$), internal (purple $\blacktriangledown$) and total (teal $\blacktriangle$) quality factors were determined. All resonators were over-coupled by design. The quality factors data follows a trend with a minimum value at around 10.2 GHz. The shape is qualitatively consistent with the simulations; although the center frequency appears shifted by roughly 350 MHz compared to the simulations. b. Aggregated coherence data of 18 qubits measured on the device. Each data point represents one coherence metric ($T_1$ in blue $\bullet$, $T_{2,Ramsey}$ in green $\bullet$, and $T_{2,echo}$ in orange $\bullet$) for one qubit, averaged over $\geq250$ measurement shots. The shaded region, bounded by the black dashed line at $\sim39$ µ s, marks the region of $T_1$'s achievable, based on our simulations, without a Purcell filter. Note how all measured $T_1$ values fall above this region.