Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2301.06364 · Physical Review Research

Circle fit optimization for resonator quality factor measurements: Point redistribution for maximal accuracy

Paul Baity, Connor Maclean, Valentino Seferai, Joe Bronstein, Yi Shu, Tania Hemakumara, Martin P. Weides

Published Mar 27, 2024• 21 citations
arXivHTMLPDF

Abstract

The control of material loss mechanisms is playing an increasingly important role for improving coherence times of superconducting quantum devices. Such material losses can be characterized through the measurement of planar superconducting resonators, which reflect losses through the resonance's quality factor Q l . The resonance quality factor consists of both internal (material) losses as well as coupling losses when resonance photons escape back into the measurement circuit. The combined losses are then described as Q l − 1 = Re { Q c − 1 } + Q i − 1 , where Q c and Q i reflect the coupling and internal quality factors of the resonator, respectively. To separate the relative contributions of Q i and Q c to Q l , diameter-correcting circle fits use algebraic or geometric means to fit the resonance signal on the complex plane. However, such circle fits can produce varied results, so to address this issue, we use a combination of simulation and experiment to determine the reliability of a fitting algorithm across a wide range of quality factor values from Q i ≪ Q c to Q c ≪ Q i . In addition, we develop a measurement protocol that can not only reduce fitting errors by factors ≳ 2 but also mitigates the influence of the measurement background on the fit results. This technique can be generalized for other resonance systems beyond superconducting resonators. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.013329

Related papers

Efficient and robust analysis of complex scattering data under noise in microwave resonators

S. Probst, F. B. Song, P. A. Bushev +2 more

Superconducting microwave resonators are reliable circuits widely used for detection and as test devices for material research. A reliable determination of their external and internal quality factors is crucial for many modern applications, which either require fast measurements or operate in the single photon regime with small signal to noise ratios. Here, we use the circle fit technique with diameter correction and provide a step by step guide for implementing an algorithm for robust fitting and calibration of complex resonator scattering data in the presence of noise. The speedup and robustness of the analysis are achieved by employing an algebraic rather than an iterative fit technique for the resonance circle.

arXiv:1410.3365•Review of Scientific Instruments•Feb 1, 2015•307 citations

An analysis method for transmission measurements of superconducting resonators with applications to quantum-regime dielectric-loss measurements

Chunqing Deng, Martin R. Otto, Adrian Lupaşcu

Superconducting resonators provide a convenient way to measure loss tangents of various dielectrics at low temperature. For the purpose of examining the microscopic loss mechanisms in dielectrics, precise measurements of the internal quality factor at different values of energy stored in the resonators are required. Here, we present a consistent method to analyze a LC superconducting resonator coupled to a transmission line. We first derive an approximate expression for the transmission S-parameter S21(ω), with ω the excitation frequency, based on a complete circuit model. In the weak coupling limit, we show that the internal quality factor is reliably determined by fitting the approximate form of S21(ω). Since the voltage V of the capacitor of the LC circuit is required to determine the energy stored in the resonator, we next calculate the relation between V and the forward propagating wave voltage Vin+, with the latter being the parameter controlled in experiments. Due to the dependence of the quality factor on voltage, V is not simply proportional to Vin+. We find a self-consistent way to determine the relation between V and Vin+, which employs only the fitting parameters for S21(ω) and a linear scaling factor. We then examine the resonator transmission in the cases of port reflection and impedance mismatch. We find that resonator transmission asymmetry is primarily due to the reflection from discontinuity in transmission lines. We show that our analysis method to extract the internal quality factor is robust in the non-ideal cases above. Finally, we show that the analysis method used for the LC resonator can be generalized to arbitrary weakly coupled lumped and distributed resonators. The generalization uses a systematic approximation on the response function based on the pole and zero which are closest to the resonance frequency. This Closest Pole and Zero Method is a valuable tool for analyzing physical measurements of high-Q resonators.

arXiv:1304.4533•Journal of Applied Physics•Aug 6, 2013•27 citations

Optimizing Interface Dielectric Loss in Superconducting Coplanar Waveguide Resonators for Improved Quantum Circuit Coherence

Omar A. Saleh, Saleem G. Rao, Mohammed Alghadeer +2 more

Superconducting quantum computing systems, including coplanar waveguide (CPW) resonators and qubits, are highly susceptible to energy dissipation from two-level systems (TLS) within bulk and interfacial dielectrics. CPW resonators serve as an ideal platform for characterizing these material losses at the single-photon excitation level. Building on recent experimental evidence that interface engineering can mitigate TLS losses, this study employs simulations to evaluate resonator quality factors across various interface modifications. Our results demonstrate that reducing losses at the substrate–air (SA) interface can increase the internal quality factor Qi by up to three orders of magnitude. While etching the SA interface also enhances Qi, material loss remains the dominant dissipation mechanism. Furthermore, we find that other lossy interfaces have a significantly smaller impact on the quality factor compared to the SA interface. These simulation results align with established experimental findings, providing a robust framework for refining resonator design. This work offers precise guidelines for TLS mitigation, essential for enhancing coherence times and developing more reliable superconducting quantum processors.

Technologies•Feb 18, 2026•0 citations

Material Loss Model Calibration for Tantalum Superconducting Resonators

Guy Moshel, Sergei Masis, Moshe Schechter +1 more

Material research is a key frontier in advancing superconducting qubit and circuit performance. In this work, we develop a simple and broadly applicable framework for accurately characterizing two-level system (TLS) loss using internal quality factor measurements of superconducting transmission line resonators over a range of temperatures and readout powers. We applied this method to a series of $α$-Ta resonators that span a wide frequency range, thus providing a methodology for probing the loss mechanisms in the fabrication process of this emerging material for superconducting quantum circuits. We introduce an analytical model that captures the loss behavior without relying on numerical simulations, enabling straightforward interpretation and calibration. Additionally, our measurements reveal empirical frequency-dependent trends in key parameters of the model, suggesting contributions from mechanisms beyond the standard tunneling model of TLSs.

arXiv:2507.12141•Jul 16, 2025•0 citations

Developing Best Practice Fabrication for Niobium Superconducting Devices

Jadrien T. Paustian

Superconducting qubits are a leading platform for scalable quantum computation. This platform offers high gate speeds and can make use of readily scalable complementary metal-oxide semiconductor (CMOS) fabrication techniques. However, superconducting qubits are susceptible to a variety of losses that arise in systems with superconductors, such as due to ubiquitous two-level systems, quasiparticles, and more. Designing fabrication processes to mitigate and manage these loss sources is critical to achieving scalable quantum computation. However, many of these loss sources are set during fabrication processing, of which there can be many different steps, each with its own parameter space. Exploring this space with qubits would be prohibitively time-consuming. Coplanar waveguide resonators provide a suitable proxy system for minimizing loss while costing less time and money to fabricate and measure. In this thesis, we explore the results of such an optimization performed on niobium resonators. Niobium is a widely used material platform for superconducting qubit circuits. We report highly consistent state-of-the-art resonator quality factors, with clear improvements over the previous fabrication recipe, and correlate the observed improvements to the internal quality factors with microstructural changes induced by hydrofluoric acid treatment, photoresist stripping, and choice of sputter deposition conditions. Additionally, we provide a detailed description of our fab process to ensure reproducibility in other lab facilities. Finally, we address some intriguing anomalies uncovered in temperature-dependent quality factors of the niobium resonators and show a correlation of the quality factors with compressive film stress.

•Dec 24, 2025•0 citations

Improving the coherence time of superconducting coplanar resonators

H. Wang, M. Hofheinz, J. Wenner +10 more

The quality factor and energy decay time of superconducting resonators have been measured as a function of material, geometry, and magnetic field. Once the dissipation of trapped magnetic vortices is minimized, we identify a power-dependent decay mechanism that is consistent with the surface two-level state model. A wide gap between the center conductor and the ground plane, as well as use of the superconductor Re instead of Al, are shown to decrease loss. We also demonstrate that classical measurements of resonator quality factor at low excitation power are consistent with single-photon decay time measured using qubit-resonator swap experiments.

arXiv:0909.0547•Applied Physics Letters•Dec 7, 2009•183 citations
The control of material loss mechanisms is playing an increasingly important role for improving coherence times of superconducting quantum devices. Such material losses can be characterized through the measurement of planar superconducting resonators, which reflect losses through the resonance's quality factor Q l . The resonance quality factor consists of both internal (material) losses as well as coupling losses when resonance photons escape back into the measurement circuit. The combined losses are then described as Q l − 1 = Re { Q c − 1 } + Q i − 1 , where Q c and Q i reflect the coupling and internal quality factors of the resonator, respectively. To separate the relative contributions of Q i and Q c to Q l , diameter-correcting circle fits use algebraic or geometric means to fit the resonance signal on the complex plane. However, such circle fits can produce varied results, so to address this issue, we use a combination of simulation and experiment to determine the reliability of a fitting algorithm across a wide range of quality factor values from Q i ≪ Q c to Q c ≪ Q i . In addition, we develop a measurement protocol that can not only reduce fitting errors by factors ≳ 2 but also mitigates the influence of the measurement background on the fit results. This technique can be generalized for other resonance systems beyond superconducting resonators. Published by the American Physical Society 2024
Superconducting microwave resonators are reliable circuits widely used for detection and as test devices for material research. A reliable determination of their external and internal quality factors is crucial for many modern applications, which either require fast measurements or operate in the single photon regime with small signal to noise ratios. Here, we use the circle fit technique with diameter correction and provide a step by step guide for implementing an algorithm for robust fitting and calibration of complex resonator scattering data in the presence of noise. The speedup and robustness of the analysis are achieved by employing an algebraic rather than an iterative fit technique for the resonance circle.
Superconducting resonators provide a convenient way to measure loss tangents of various dielectrics at low temperature. For the purpose of examining the microscopic loss mechanisms in dielectrics, precise measurements of the internal quality factor at different values of energy stored in the resonators are required. Here, we present a consistent method to analyze a LC superconducting resonator coupled to a transmission line. We first derive an approximate expression for the transmission S-parameter S21(ω), with ω the excitation frequency, based on a complete circuit model. In the weak coupling limit, we show that the internal quality factor is reliably determined by fitting the approximate form of S21(ω). Since the voltage V of the capacitor of the LC circuit is required to determine the energy stored in the resonator, we next calculate the relation between V and the forward propagating wave voltage Vin+, with the latter being the parameter controlled in experiments. Due to the dependence of the quality factor on voltage, V is not simply proportional to Vin+. We find a self-consistent way to determine the relation between V and Vin+, which employs only the fitting parameters for S21(ω) and a linear scaling factor. We then examine the resonator transmission in the cases of port reflection and impedance mismatch. We find that resonator transmission asymmetry is primarily due to the reflection from discontinuity in transmission lines. We show that our analysis method to extract the internal quality factor is robust in the non-ideal cases above. Finally, we show that the analysis method used for the LC resonator can be generalized to arbitrary weakly coupled lumped and distributed resonators. The generalization uses a systematic approximation on the response function based on the pole and zero which are closest to the resonance frequency. This Closest Pole and Zero Method is a valuable tool for analyzing physical measurements of high-Q resonators.
Superconducting quantum computing systems, including coplanar waveguide (CPW) resonators and qubits, are highly susceptible to energy dissipation from two-level systems (TLS) within bulk and interfacial dielectrics. CPW resonators serve as an ideal platform for characterizing these material losses at the single-photon excitation level. Building on recent experimental evidence that interface engineering can mitigate TLS losses, this study employs simulations to evaluate resonator quality factors across various interface modifications. Our results demonstrate that reducing losses at the substrate–air (SA) interface can increase the internal quality factor Qi by up to three orders of magnitude. While etching the SA interface also enhances Qi, material loss remains the dominant dissipation mechanism. Furthermore, we find that other lossy interfaces have a significantly smaller impact on the quality factor compared to the SA interface. These simulation results align with established experimental findings, providing a robust framework for refining resonator design. This work offers precise guidelines for TLS mitigation, essential for enhancing coherence times and developing more reliable superconducting quantum processors.
Material research is a key frontier in advancing superconducting qubit and circuit performance. In this work, we develop a simple and broadly applicable framework for accurately characterizing two-level system (TLS) loss using internal quality factor measurements of superconducting transmission line resonators over a range of temperatures and readout powers. We applied this method to a series of ααα-Ta resonators that span a wide frequency range, thus providing a methodology for probing the loss mechanisms in the fabrication process of this emerging material for superconducting quantum circuits. We introduce an analytical model that captures the loss behavior without relying on numerical simulations, enabling straightforward interpretation and calibration. Additionally, our measurements reveal empirical frequency-dependent trends in key parameters of the model, suggesting contributions from mechanisms beyond the standard tunneling model of TLSs.
Superconducting qubits are a leading platform for scalable quantum computation. This platform offers high gate speeds and can make use of readily scalable complementary metal-oxide semiconductor (CMOS) fabrication techniques. However, superconducting qubits are susceptible to a variety of losses that arise in systems with superconductors, such as due to ubiquitous two-level systems, quasiparticles, and more. Designing fabrication processes to mitigate and manage these loss sources is critical to achieving scalable quantum computation. However, many of these loss sources are set during fabrication processing, of which there can be many different steps, each with its own parameter space. Exploring this space with qubits would be prohibitively time-consuming. Coplanar waveguide resonators provide a suitable proxy system for minimizing loss while costing less time and money to fabricate and measure. In this thesis, we explore the results of such an optimization performed on niobium resonators. Niobium is a widely used material platform for superconducting qubit circuits. We report highly consistent state-of-the-art resonator quality factors, with clear improvements over the previous fabrication recipe, and correlate the observed improvements to the internal quality factors with microstructural changes induced by hydrofluoric acid treatment, photoresist stripping, and choice of sputter deposition conditions. Additionally, we provide a detailed description of our fab process to ensure reproducibility in other lab facilities. Finally, we address some intriguing anomalies uncovered in temperature-dependent quality factors of the niobium resonators and show a correlation of the quality factors with compressive film stress.
The quality factor and energy decay time of superconducting resonators have been measured as a function of material, geometry, and magnetic field. Once the dissipation of trapped magnetic vortices is minimized, we identify a power-dependent decay mechanism that is consistent with the surface two-level state model. A wide gap between the center conductor and the ground plane, as well as use of the superconductor Re instead of Al, are shown to decrease loss. We also demonstrate that classical measurements of resonator quality factor at low excitation power are consistent with single-photon decay time measured using qubit-resonator swap experiments.