Filter synthesis for wideband parametric amplifier and converter design

Low noise amplification is a critical element in dispersive readout approaches in superconducting quantum computing. Although the best noise performance is obtained in reflection parametric amplifiers (e.g., Josephson parametric amplifiers (JPAs), Josephson ring modulators (JRMs), etc.), this has come at the expense of having meager bandwidths in comparison to traveling wave parametric amplifiers (TWPAs). While there have been a number of demonstrations showing how the bandwidth can be increased, the reasoning has largely been based on physicist-centric reasoning that is often difficult to translate into a systematic design methodology that can be extended to more complicated devices. This includes, for instance, circuit designs that might include parametric frequency conversion or nonreciprocity. Meanwhile, the techniques for synthesizing wideband parametric amplifiers were already articulated in the 1960s in the context of varactor (modulated capacitor)-based low noise parametric amplifiers (c.f., G.L. Matthaei, L. Young, and E.M. Jones. "Design of Microwave Filters, Impedance-Matching Networks, and Coupling Structures. Volume 2," Stanford Research Inst Menlo Park CA (1963)). These are closely related to wideband matching circuit synthesis and filter design techniques that are well-known in modern electrical engineering. In this talk, I will discuss the links between these disparate approaches and outline the basic reasoning and methodology for synthesizing more complex parametric circuit designs for wideband parametric amplifiers and frequency converters using modulated inductances such as Josephson junctions and kinetic inductance elements (see O. Naaman, and J. Aumentado, "Synthesis of Parametrically Coupled Networks." PRX Quantum 3.2 020201 (2022)).