Symbolic-Numeric Modeling of Resonant Phase Matching for Dispersion Engineering in Josephson Traveling-Wave Parametric Amplifiers

Superconducting traveling-wave parametric amplifiers are a key technology for high-fidelity qubit readout. Due to their quantum-limited noise performance and the ultra-low-power signals in quantum circuits, field quantization needs to be taken into account for accurate modeling of these devices. We present a symbolic-numeric modeling approach for the analysis of Josephson traveling-wave parametric amplifiers, including resonant phase matchers. We demonstrate the capabilities of our approach by comparing the results to existing analytical models from the literature and present first results beyond the stiff pump approximation.