Numerical simulations of Josephson Traveling Wave Parametric Amplifiers (JTWPAs): comparative study of open-source tools

Josephson Traveling Wave Parametric Amplifiers (JTWPAs) are largely exploited in quantum technologies for their broadband and low noise performance in the microwave regime. When one or more microwave tones are applied at the input, such devices show a complex wave-mixing response due to their intrinsic nonlinear nature. Numerical simulations of the JTWPAs nonlinear behaviour provide useful insights not only for the design of such devices, but also for the interpretation and validation of the experimental results. Here we present and discuss a comparative analysis of different open-source tools which can be used for JTWPAs numerical simulations. We focus on two tools for transient simulations, WRSPICE and PSCAN2, and on one tool for direct simulation of the frequency domain behaviour, JosephsonCircuit.jl. We describe the working principle of these three tools and test them considering as a benchmark a JTWPA based on SNAILs (Superconducting Nonlinear Asymmetric Inductive eLement) with realistic experimental parameters. Our results can serve as a guide for numerical simulations of JTWPAs with open-source tools, highlighting advantages and disadvantages depending on the simulation tasks.