Modeling and Harmonic Balance Analysis of Superconducting Parametric Amplifiers for Qubit Readout: A Tutorial

The parametric modulation of reactive elements in circuits for amplification dates back to World War I, when Alexanderson and others proposed magnetic amplifiers for radio transmitters [1], [2], [3], [4]. The low-noise figure of the first parametric amplifiers, as a result of using passive elements, was on par with the standard at the time [5].