A Quantum Model for the Added Noise in SNAIL Traveling-Wave Parametric Amplifiers

Broadband cryogenic traveling-wave parametric amplifiers are vital components for the readout of superconducting qubits. This is due to their large gain and quantum-limited noise performance. In this paper, we present analytic solutions for the equivalent added input fluctuations of state-of-the-art traveling-wave parametric amplifiers based on superconducting nonlinear asymmetric elements derived from a quantum mechanical model, including losses and dispersion.