Time Domain Design of a Josephson Parametric Amplifier and Comparison with Input Output Theory

Quantum-limited amplifiers, such as Josephson Traveling Wave Parametric Amplifiers (JTWPAs) and Joseph- son Parametric Amplifiers (JPAs), are essential components in quantum computers. They amplify low-power microwave signals from qubits at the 10 mK stage before further amplification at the 4 K stage using HEMT amplifiers. In JPAs, parametric amplification is based on the nonlinear properties of Josephson Junctions. While JPAs are typically designed and analyzed using input-output theory based on quantum physics, we propose an alternative approach based on an equivalent circuit model of JPAs, implemented using open-source Josephson circuit simula- tors. We compare the results with those obtained from input- output theory. This method enables the use of circuit optimizers for various objective functions and significantly reduces design time compared to quantum theory-based approaches.