Optimizing the scattering and stability of matched nonreciprocal Josephson parametric amplifiers

High-fidelity, frequency-multiplexed qubit measurement is essential for error correction and feedback in large-scale quantum computing. Optimizing the first-stage amplifier is critical to reduce circulator count in the readout chain and minimize amplified noise propagating back to the readout resonator. Key requirements include stability, impedance matching, high forward gain, and minimal reverse gain. Meeting these requirements in resonant parametric amplifiers creates a delicate tradeoff between the matching of the device and the forward gain over the entire bandwidth of the device. We present a design procedure that gives an intuitive picture of how this tradeoff works and facilitates the optimization of a particular topology. We demonstrate the application of this procedure in the design and simulation of a matched, stable, nonreciprocal parametric amplifier exhibiting an instantaneous bandwidth of 500 MHz.