Microwave Package Design for Superconducting Quantum Processors

Solid-state qubits with transition frequencies in the microwave regime, such as superconducting qubits, are at the forefront of quantum information processing. However, high-fidelity, simultaneous control of superconducting qubits at even a moderate scale remains a challenge, partly due to the complexities of packaging these devices. Here, we present an approach to microwave package design focusing on material choices, signal line engineering, and spurious mode suppression. We describe design guidelines validated using simulations and measurements used to develop a 24-port microwave package. Analyzing the qubit environment reveals no spurious modes up to 11 GHz. The material and geometric design choices enable the package to support qubits with lifetimes exceeding $350\mu \mathrm{s}$. The microwave package design guidelines presented here address many issues relevant for near-term quantum processors.

Popular Summary

Quantum computers hold the promise to solve specific computational problems significantly faster than contemporary devices. Solid-state qubits that rely on microwave control to operate are among the leading candidates for realizing useful near-term quantum processors, but significant engineering challenges constrain these devices from scaling up further. In particular, qubits require a precisely engineered microwave environment to suppress energy decay and corresponding information loss. For instance, the corruption of information can occur due to lossy package modes interacting with the qubit. As the number of qubits increases, qubit packages must be adapted to support an increasing number of control lines without creating additional loss channels.

We present a ground-up approach to package design that addresses these challenges in the context of a multiqubit quantum processor, focusing specifically on maintaining high simultaneous control fidelity and coherence times for a system with many control lines. We also explore the extent to which device packaging, particularly for multiple qubits, is currently limiting qubit coherence times. We perform a comprehensive evaluation of the package-related loss channels and demonstrate that lossy package modes can lead to coherence limits within an order of magnitude of today’s state-of-the-art qubit coherence times, underscoring the importance of high-performance package engineering.

This work provides an important step towards the implementation of larger, near-term quantum information processors and in understanding how to provide efficient control lines while maintaining high qubit coherence.

Figure 1

Package environment, layout, and requirements. (a) Dilution refrigerator with multiple temperature stages holding the qubit chip enclosed in a microwave package. The microwave package interfaced with through microwave lines is mounted on a cold finger in the mixing chamber reaching a base temperature of approximately 10 mK. (b) The microwave package consists of a metal enclosing, microwave connectors, an interposer for signal fan out, and a microwave cavity in the center surrounding the quantum chip. (c) The purpose of a microwave package is to shield the enclosed qubit chip from external radiation (red oscillating arrow) and stray magnetic fields (yellow lines) while providing impedance-matched (transmitted green pulse and reflected blue pulse at the input and output), low-crosstalk communication channels (crosstalk in green at input), and a thermal link to the dilution refrigerator.

Figure 2

Interposer design. (a) Interposer layout for a 24-line package fabricated out of a three-layer Rogers 4350 controlled impedance glass-reinforced ceramic laminate. Stripline-based waveguides with dense via shielding are utilized to reduce signal crosstalk. (b) EM simulation [three-dimensional (3D) finite element simulation software comsol Multiphysics] of a via transition used for subminiature push-on- (SMP) type microwave connectors. The transition is impedance matched (not shown) to minimize reflections and effects on the step response. (c) Picture of a $5\times 5{\mathrm{mm}}^2$ qubit chip mount with signal launches in the periphery. Wirebonds are used to provide signal connections and ground the device. (d),(e) Measured nearest-neighbor and next-nearest-neighbor crosstalk. A high-port count network analyzer using Keysight M9374A PXIe modules is used to obtain the full scattering matrix. All transmission parameters corresponding to signal crosstalk information are overlaid on the plots. The purple background fading out with increasing frequency indicates the decreasing relevance of modes as their frequency separation to the qubit transition frequency increases. Note that the separate group of traces with greater isolation, as highlighted in (d),(e), correspond to crosstalk that is reduced at corners of the package, as indicated by the pairs of blue lines in (a).

Figure 3

Wirebond design. (a) Diagram of a chip (gray) with four transmission lines wirebonded to an interposer (beige) surrounding it. The instigating line, indicated in purple, can lead to near-end crosstalk (NEXT) and far-end crosstalk (FEXT) in the disturbed line, shaded red and blue, respectively. (b) Schematic representation of a wirebond interconnect and its lumped element model. The flares located on the ends of the interposer and chip’s transmission lines, as highlighted by the dashed box in (a), correspond to the two tuning capacitors to ground, while the wirebond forms the series inductance. Note that the wirebonds used to connect the signal lines are spread out in a $\mathsf{V}$ shape to minimize mutual inductance. (c) Plot of maximum inductance compensation versus cutoff frequency for Butterworth and Chebyshev filter designs, with 1 nH roughly corresponding to 1 mm in wirebond length. (d),(e) The effect of wirebond configuration on signal crosstalk. A simplified model with the same spatial dimensions as the 24-pin design is employed to simulate the relative reduction of signal wirebond crosstalk with the addition of more grounding wirebonds. As the number of grounding wirebonds increases, the electric field strength between the chip ground and the package cavity rapidly decreases, resulting in the suppressed coupling between adjacent signal wirebonds.

Figure 4

Package mode measurements and simulation. (a) Package modes are probed at liquid nitrogen temperature using a multiport vector network analyzer. The scattering matrix elements corresponding to transmission across the package cavity, as measured via the ports marked green in (b), are overlaid (gray) and averaged (dark purple). (b) EM simulations reveal eigenmodes at 11.1 GHz (orange) and 18.1 GHz (purple), which correspond well with the measured peaks as marked by the correspondingly colored vertical lines in (a). The purple background fading out with increasing frequency in (a) indicates the decreasing relevance of modes as their frequency separation to the qubit transition frequency increases.

Figure 5

Experimental package mode characterization. (a) Basic setup to measure fixed-frequency transmon qubits with individual readout resonators coupling to a common transmission line. In the following panels, the results of the qubit and resonator indicated with a yellow dashed rectangle are explicated. (b) The qubit has an average qubit lifetime of $T_1\approx 121.4\mu \mathrm{s}$ and coherence time of $T_2^{\ast }\approx 53.2\mu \mathrm{s}$ measured in intervals across a period of 12 h. (c),(d) The microwave environment between 2 and 20 GHz registered by the qubit is mapped out using the qubit itself as a sensor and a continuous-wave probe tone—added to the qubit readout and control signal—interacting with the qubit microwave environment. Probe-tone-dependent indirect and direct effects on the qubit are recorded using Ramsey spectroscopy. In both the time-domain (c) and frequency-domain (d) panels, the qubits, readout resonators, and the ground to third excited state transition are identifiable as shifts in the Ramsey frequency. Furthermore, four features between 11 and 18 GHz can be identified. The following mode characterization procedure is exemplified on the fourth mode, shown augmented again in (e) at 17.19 GHz. (f) The linewidth of a mode $\kappa /(2\pi )$ is the full width at half maximum (FWHM) of the Fourier transformed frequency-dependent Ramsey scan, here 20 MHz. (g) The Ramsey frequency change as the power of the probe tone—parked at the mode’s resonance frequency, here at 17.189 GHz—is varied. The power is measured at the signal generator. (h) The qubit dephasing as a result of the varying probe tone power is extrapolated by performing fits to $T_2^{\ast }$ experiments, as shown in the example in panel (b). The presented analysis yields a coupling rate of $g/2\pi \approx 17.73\mathrm{MHz}$ for mode IV. Note that, for the measurements shown in (c)–(h), the traveling-wave parametric amplifier is bypassed to prevent interference with the probe tone.

Figure 6

Schematic diagram of the interposer stackup configuration (not to scale). The board consists of two Rogers 4350 cores bonded by a layer of FEP film, indicated in purple. Through vias are used for grounding and shielding, whereas blind vias are utilized for signal routing to minimize parasitic resonances.

Figure 7

Single-ended TDR measurement of the SMP-to-interposer connector transition. The reference plane of the connector is located at 0 ns. The wirebond launch is left open (no chip connected), resulting in a steep increase in impedance.

Figure 8

Measurement setup used to obtain the mode profile of the package. The control, readout, and probe signals are combined and sent down the dilution refrigerator with a total of 60 dB of attenuation distributed at various stages (not shown). The readout signal is amplified by a traveling-wave parametric amplifier (TWPA) at the 10 mK stage, a high-electron-mobility transistor (HEMT) amplifier at the 3 K stage, and a low noise amplifier at room temperature before being down-converted and subsequently digitized. Note that the TWPA can be bypassed if necessary.

Figure 9

Experimental package mode evaluation using four qubits. The Ramsey spectra are taken simultaneously from four different qubits while a probe tone is injected through the central transmission line. Note the similarity between the spurious modes (indicated by yellow arrows) measured by qubits 1 and 3, as well as qubits 2 and 4. The orange lines indicate qubit-related features which shift depending on the sensor qubit used.