A method to form a cascading microwave directional amplifier (cascade), the method comprising:
- fabricating a set of Josephson devices, each Josephson device in the set having a corresponding operating bandwidth of microwave frequencies, wherein different operating bandwidths have different corresponding center frequencies;
- and
- forming a series coupling between first Josephson device from the set and an nth Josephson device from the set, wherein the series coupling causes
- the first Josephson device to amplify a signal of a first frequency from a frequency multiplexed microwave signal (multiplexed signal) and propagate without amplification a signal of an nth frequency from the multiplexed signal in a first signal flow direction through the series coupling, and
- the nth Josephson device to amplify the signal of the nth frequency and propagate without amplification the signal of the first frequency from the multiplexed signal in the first signal flow direction through the series.