Rational function regression methods for resonator spectroscopy analysis

The spectroscopy of a resonator contains all the parameters required to describe its response. In practice, this is done by probing the resonator with an electromagnetic wave and recording the quadratures of its reflection. This protocol results in a noisy measurement of the complex scattering parameter. By adjusting the parameters of a rational function to the data acquired when sweeping the frequency, essential properties of the resonator—such as its internal quality factor and coupling to the drive line—can be determined.

While several numerical techniques exist to tackle this specific problem, such as SK-iteration and Vector fitting, in practice, in the cQED community, these techniques are rarely known. In comparison to the state of the art, the many existing heuristic routines often lack robustness.

In this work, we present a comparison of various rational function fitting methods applied to resonator spectroscopy. In particular, we run a sensitivity and failure mode analysis for each method and study the impact of noise on the extracted response parameters.