We detail recent advances in Josephson junction based parametricamplifiers, including traveling wave and impedance engineered cavitybased amplifiers. We provide an overview and tutorial on usingJosephsonCircuits.jl, our Julia package for high performance simulationsof the gain and quantum efficiency of arbitrary circuits containingJosephson junctions, including the impact of an arbitrary number ofpump, signal, and idler modes, as well as dielectric loss. We describehow Floquet mode traveling wave parametric amplifiers suppress thegeneration of unwanted modes, yielding higher quantum efficiency andless sensitivity to the impedance environment outside of theamplification band. Finally, we describe our progress towards realizingnear ideal quantum efficiency Floquet mode Josephson traveling waveparametric amplifiers in a low loss aluminum process.

Keywords: Qubit