Nonlinear Elements in Traveling-Wave Parametric Amplifiers for Dispersive Qubit Readout

In this paper, we present models for the nonlinearity of different nonlinear elements for superconducting Josephson traveling-wave parametric amplifiers. Such devices are typically used as a first-stage readout amplifier for superconducting qubits in a cryogenic quantum computing environment. The nonlinear coefficients of different designs are evaluated as functions of an externally applied bias field, taking into account direct and external pumping schemes. Finally, we present results of the total gain for two different nonlinear transmission lines, one that is embedded with single Josephson junctions operating in four-wave mixing mode with direct pumping, and an externally pumped SNAIL-based amplifier operating in the three-wave mixing regime with a corresponding constant external flux bias. The gain is evaluated using a quantum circuit model including substrate losses and chromatic dispersion.