Reconfigurable Superconducting Quantum Circuits Enabled by Micro-Scale Liquid-Metal Interconnects

Abstract

Modular architectures are a promising route toward scalable superconducting quantum processors, but finite fabrication yield and the lack of high quality temporary interconnects impose fundamental limitations on system size. Here, we demonstrate chip-scale liquid-metal interconnects that show promise for plug-and-play superconducting quantum circuits by enabling non-destructive module replacement while maintaining high microwave performance. Using gallium-based liquid metals, we realize high-quality inter-module signal and ground interconnects, comparable in performance to conventional coplanar waveguide resonators. We illustrate consistent device characteristics across three thermal cycles between room temperature and 15 mK, as well as the ability to reform superconducting connections following module replacement. A width-dependent resonance frequency shift reveals a significant kinetic inductance fraction, which we attribute to the presence of $β$-phase tantalum as confirmed by X-ray characterization. Finally, we investigate power-dependent loss mechanisms and observe high-power dissipative nonlinearities qualitatively consistent with a readout-power heating model. These results establish liquid metals as viable chip-scale interconnects for reconfigurable, modular superconducting quantum systems.

Figures (19)

• Figure 1: Example of a modular liquid-metal-enabled quantum system. The qubit chips and interposer chips are connected by superconducting liquid-metal bumps (gray). The adjacent half-bus resonators (cyan meandered line) on the interposer chips are bridged laterally by liquid metal at the chip edges. The qubit chips are self-spaced, self-aligned, and connected/grounded by liquid metal droplets in a flip-chip architecture. The qubit bus resonators (blue meandered line) are capacitively coupled to the qubits (blue parallel bars) and connected to the interposer by liquid metal on the other end. Non-destructive replacement of modules at room temperature is enabled by the liquid nature of the interconnects.
• Figure 2: The chip assembly design: The top chip layout and material stack of the chip assembly are shown in (a) and (b), respectively. In the layout, the smaller chip at the top is chip A. It consists of four half-wavelength resonators, each extended from the matching edge. The larger chip at the bottom is chip B, which contains the other four halves of the resonator, all with matching edges and complementary shapes, allowing them to align with the four halves on chip A. The other four continuous resonators serve as control resonators. (c) Zoom-ins of the LM pads shown in (a). To prepare for the subsequent liquid metal deposition, 25-by-50 $\mathrm{\mu m}$ gold-on-titanium pads are defined at the end of where the center strips of half-resonators meet the matching edge. Identical ground pads are also defined with less than 500 $\mathrm{\mu m}$ pitch size. (d) Zoom-ins of the vernier scale markers shown in (a). The vernier scale markers at the edges of adjacent chiplets visualize the lateral alignment. (e) The LM droplets adhere to the gold pad shapes. (f) The alignment accuracy is within $\pm$2 $\mathrm{\mu m}$, visualized by the aligned central markers.
• Figure 3: The loss of LM and control resonators for open- and short-ended resonators. (a) The total loss at low power, 15 mK. The heights of the bars denote the sample mean of the loss. The colors of the bars depict the type of loss, where the orange bars are TLS loss and the blue bars are power-independent loss. The $x$-axis labels read the type of the resonators, either open- or short-ended resonators, and the colors of the labels represent whether the samples are LM (red) or control (black) resonators. The error bars centered at the top of each stacked bar are the standard errors of the sample mean. The black error bars are for power-independent loss, and the grey error bars are for TLS loss. The number of samples for each type is labeled above the corresponding bar. (b) The schematic of open- and short-ended resonators with the LM droplets at $\lambda/4$. The lefthand cartoon is the open-ended resonators, where the $\lambda/4$ section exhibits the strongest magnetic field at the fundamental mode. The righthand one is the short-ended resonators, where the $\lambda/4$ section exhibits the strongest electric field.
• Figure 4: The total loss of LM and control resonators for open- and short-ended resonators at low power, 15 mK. The bar heights and colors denote the sample mean and type of loss, respectively, where blue bars represent power-independent loss and orange bars represent TLS loss. The number above each bar represents the number of samples. The lengths of the black and grey error bars indicate the standard errors of the sample means for the power-independent loss and TLS loss, respectively. The labels on the $x$ axis indicate the category of resonators, whether they are open- or short-ended, and whether they are LM (red) or control (black). Each category contains three bars, representing the first, second, and third measurements in chronological order from left to right. The first and third measurements are two months apart.
• Figure 5: Resistance measurements before and after replacing modules. (a) The normalized resistance vs. temperature. The measurement starts at the base temperature of 3 K and gradually increases the temperature of the cold finger at a sufficiently low rate (1 mK/s). The colors represent whether the measurement is conducted before (black) or after (orange) the module replacement. (b)--(d) The photographs of the module replacement flow. (b) shows the LM interconnect between chips 1 and 2, and the resistance of this LM interconnect is indicated by the black data points in (a). (c) was taken after removing chip 2 and installing chip 4. The gold pads are used to define the LM shape. (d) Reconnecting the LM interconnect across chip 1 and the newly installed chip 4 (orange data points). The discrepancy of the resistance curve between the two measurements is likely due to the slight composition change in the LM interconnect induced by the HCl solution treatment for residue removal.