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IEEE Transactions on Applied Superconductivity

Design and Modeling of Double-Fold Superconducting High-Q Coplanar Waveguide Resonators for Quantum Applications

Jagmohan Singh, Hongxiang Shen, Nobuyuki Yoshikawa, P. Suggisetti, Darshak Bhatt

Published Sep 1, 2025• 3 citations
Publisher

Abstract

In this paper, we present a novel design of a compact, double-fold half-wave superconducting coplanar waveguide resonator, specifically optimized for quantum readout. The geometry offers advantages in terms of scalability and allows for a more compact integration of qubits per unit area. The superconducting resonators are designed to operate within a fundamental frequency range of 1.9 GHz$-$1.95 GHz, utilizing both gap and finger coupling schemes. The devices are fabricated using thin aluminum films deposited on high-resistivity sapphire substrates. The proposed resonators exhibit quality factor (Q$_{L}$) of 2.9 ×$ 10^{5}$and 1.58 ×$10^{3}$for gap coupled and finger coupled, respectively, during experimental measurements. The simulated Q$_{L}$of single-folded meander line resonators are found to be 4.65 ×$10^{5}$and 258.42, for gap coupled and finger coupled, respectively, for comparison purpose at similar operating frequency. A comprehensive analysis of the microwave transmission spectra was conducted at cryogenic temperatures near 10 mK, across very high input drive powers ($-$30 dBm to$-$10 dBm). Experimental results show a good agreement with simulations and the equivalent lumped circuit model. Notably, the proposed design reduces the physical footprint of the resonator devices up to 28.2$\%$compared to conventional single-fold meandered structures. The resonators demonstrate strong potential for integrating qubits with readout and control buses in quantum information processing which require a Q$_{L}$between$10^{4}$$-$$10^{5}$. They also being well-suited for cryogenic detector applications that utilize microwave kinetic inductance detector (MKID) arrays in frequency multiplexing for different coupling schemes.

DOI
10.1109/tasc.2025.3605024

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In this paper, we present a novel design of a compact, double-fold half-wave superconducting coplanar waveguide resonator, specifically optimized for quantum readout. The geometry offers advantages in terms of scalability and allows for a more compact integration of qubits per unit area. The superconducting resonators are designed to operate within a fundamental frequency range of 1.9 GHz−-−1.95 GHz, utilizing both gap and finger coupling schemes. The devices are fabricated using thin aluminum films deposited on high-resistivity sapphire substrates. The proposed resonators exhibit quality factor (QL_{L}L​) of 2.9 ×105 10^{5}105and 1.58 ×10310^{3}103for gap coupled and finger coupled, respectively, during experimental measurements. The simulated QL_{L}L​of single-folded meander line resonators are found to be 4.65 ×10510^{5}105and 258.42, for gap coupled and finger coupled, respectively, for comparison purpose at similar operating frequency. A comprehensive analysis of the microwave transmission spectra was conducted at cryogenic temperatures near 10 mK, across very high input drive powers (−-−30 dBm to−-−10 dBm). Experimental results show a good agreement with simulations and the equivalent lumped circuit model. Notably, the proposed design reduces the physical footprint of the resonator devices up to 28.2%\%%compared to conventional single-fold meandered structures. The resonators demonstrate strong potential for integrating qubits with readout and control buses in quantum information processing which require a QL_{L}L​between10^{4}$$-$$10^{5}. They also being well-suited for cryogenic detector applications that utilize microwave kinetic inductance detector (MKID) arrays in frequency multiplexing for different coupling schemes.
We report our development on design, fabrication and characterization of various superconducting resonators for quantum device applications. The resonators are developed mainly for superconducting qubit implementation in circuit QED structure, but future application will include photon detectors such as microwave kinetic inductance detectors. First we designed and fabricated half-wavelength coplanar waveguide resonators with niobium thin film on a high resistive silicon wafer, with the fundamental frequencies in the range of 1 to 8 GHz. The loaded quality factors are controlled by the coupling capacitors, and the lower bound of the intrinsic quality factor was measured down to 7 mK in the dilution refrigerator. We have also designed quarter-wavelength resonators and lumped LC resonators coupled to a transmission line, and characterized multiple resonators in a single transmission line. For the 3D transmon qubit application, we designed and fabricated a rectangular box resonator with superconducting aluminum. The intrinsic quality factor of the box resonator exceeds three million at 7 mK. We will also present basic results on the integration of a transmon qubit in the superconducting resonator.
High quality on-chip microwave resonators have recently found prominent new applications in quantum optics and quantum information processing experiments with superconducting electronic circuits, a field now known as circuit quantum electrodynamics (QED). They are also used as single photon detectors and parametric amplifiers. Here we analyze the physical properties of coplanar waveguide resonators and their relation to the materials properties for use in circuit QED. We have designed and fabricated resonators with fundamental frequencies from 2 to 9 GHz and quality factors ranging from a few hundreds to a several hundred thousands controlled by appropriately designed input and output coupling capacitors. The microwave transmission spectra measured at temperatures of 20 mK are shown to be in good agreement with theoretical lumped element and distributed element transmission matrix models. In particular, the experimentally determined resonance frequencies, quality factors, and insertion losses are fully and consistently explained by the two models for all measured devices. The high level of control and flexibility in design renders these resonators ideal for storing and manipulating quantum electromagnetic fields in integrated superconducting electronic circuits.
The use of a transmission line resonator offers the possibility for different sensor readout methods, e.g. flux qubit and kinetic inductance detectors. Both cases require a high quality factor, Q L , of the cavity circuit to detect small deviations in the resonance frequency. Various superconducting niobium coplanar waveguide resonators of λ/4 and λ/2 wavelength for 3 and 6 GHz were developed. Different layouts for the coplanar resonators were designed, simulated and measured on common silicon and sapphire substrates at 4.2 K. We found a very good agreement between simulation and measurement results, with Q L between 10 4 and 10 5 at helium temperatures. The presented results show the dependences on the chosen cross section geometries, the coupling factor and the complex layout of the transmission line.
We successfully designed and fabricated an absorption-type of superconducting coplanar waveguide (CPW) resonators. The resonators are made from a niobium film (about 160 nm thick) on a high-resistance Si substrate, and each resonator is fabricated as a meandered quarter-wavelength transmission line (one end is short to the ground and another end is capacitively coupled to a through feedline). With a vector network analyzer we measured the transmissions of the applied microwave through the resonators at ultra-low temperature. The obtained loaded quality factors are significantly high, i.e. up to ∼10 6 . When the temperature increases slowly from the base temperature (20 mK), the resonance frequencies of the resonators are blue shifted and the quality factors are lowered slightly. In principle, this type of device can integrate a series of CPW resonators with a common feedline, making it a promising candidate as the data bus for coupling distant solid-state qubits and the sensitive detector of single photons.
Abstract The coplanar waveguide (CPW) microwave resonators have been widely applied for solid-state quantum computation and single-photon detection. Based on the physical analysis for the high fidelity readouts of the qubit(s), in this paper we design and then fabricate accordingly the desired aluminum (Al) film quarter-wavelength resonators on sapphire substrates. The ultra-low temperature measurement results show that the linearity of the internal quality factor under the proper driving power is satisfied well for the high fidelity readouts of the qubit(s); and the phase- and amplitude fractional frequency noises are significantly less for avoiding the potential information false alarms of the detected qubit during the readouts. With the demonstrated qubit-resonator experimental parameters, we argue that the designed and fabricated quarter-wavelength CPW resonators, with optimized parameters, can be used to implement the desired weakly perturbing readout measurements of the solid-state qubits on-chip.
Superconducting quantum chips commonly utilize quarter-wavelength (λ/4) transmission line resonators as readout circuits. An analytical model for the accurate determination of resonance frequencies and coupling Q-factors of feedline-coupled superconducting resonators is introduced. The model leverages four-port microwave network analysis, integrating boundary conditions and conformal mapping techniques to compute even- and odd-mode impedances in edge-coupled coplanar waveguide (CPW) structures. Its versatility allows application to both planar and 3-D heterogeneous architectures, making it a powerful tool for resonator design. To validate the model, a test chip with λ/4 resonators of varying geometries is fabricated and measured in a cryogenic environment. Comparisons with finite element method (FEM) simulations and experimental measurements confirm the model's accuracy, with resonance frequencies and coupling Q-factors aligning closely across configurations. This proposed model facilitates the design of superconducting resonators in readout circuits for more effective, scalable, and adaptable quantum computing architectures.