Broadband design of parametric non-reciprocal devices

There has been significant recent progress in understanding parametric non-reciprocal devices such as circulators and directional amplifiers based on superconducting Josephson circuits. However, these devices remain of limited practical utility due to their narrow bandwidths - typically in the 10's of MHz. To be useful for multiplexed readout in intermediate scale quantum processors, we must engineer these devices to meet prescribed bandwidth and transmission characteristics. In this talk, we outline a procedure for designing parametric devices with bandwidths up to ~1 GHz. We give design examples for a broadband parametric circulator with better than 20 dB isolation over a 500 MHz band, and a non-reciprocal parametric amplifier with broadband reverse isolation and 20 dB forward gain. We illustrate the devices' predicted performance with simulation of their S-parameters.