Circle fit optimization for resonator quality factor measurements

The mitigation of material losses is playing an increasingly important role for improving coherence times of superconducting quantum devices [1,2]. 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 external losses when resonance photons escape into the measurement circuit. The combined losses are then described as Q_l^-1 = Q_c^-1 + Q_i^-1, where Q_c and Q_i reflect the external and internal quality factors of the resonator, respectively. The resonance response projects onto the complex plane as circle, which can be fit by geometric or algebraic means [3,4] to extract the resonator’s quality factors. Diameter-correcting circle fits, such as those developed by Probst et al. [5], use algebraic means to distinguish the internal and external quality factor contributions. However, such circle fits can produce varied results [6]. To address this issue, we have used a combination of simulation and experiment to determine the reliability of the fitting algorithm of Probst et al. across a wide range of quality factor values from Q_ici depends on the ratio Q_i/Q_c, Q_i fits can still be accurate and reliable when noise levels are low and the number of data points remains large. In addition, we have also explored sources of fit bias and have developed alternative measurement protocols to minimize the effects of such bias from the measurement background on resonance circle fit parameters.

[1] C. R. H. McRae et al. Rev. Sci. Instrum. 91, 091101 (2020).

[2] Conel E. Murray, Materials Science & Engineering R 146, 100646 (2021).

[3] Paul J. Petersan and Steven M. Anlage, Journal of Applied Physics 84, 3392 (1998).

[4] N. Chernov and C. Lesort, J. Math. Imaging Vision 23, 239 (2005).

[5] Probst et al. Review of Scientific Instruments 86, 024706 (2015).

[6] C. R. H. McRae, 2022 IEEE/MTT-S International Microwave Symposium - IMS 2022, 230 (2022).