This thesis develops theory for and experimentally demonstrates a new way to break Lorentz\ reciprocity\textendash\textendashthe symmetry, in an electrical network, under exchange of source and detector. The\ approach is based on the sequential application of frequency conversion and delay; as frequency\ and time are Fourier duals, these operations do not generally commute. We apply this method in\ the construction of an on-chip superconducting microwave circulator, a critical component for the\ unidirectional routing of quantum information in superconducting networks. The device requires\ neither permanent magnets nor microwave control tones, allowing on-chip integration with other\ superconducting circuits without expensive control hardware. Isolation in the device exceeds 20\ dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at\ select operation frequencies. Furthermore, the device is linear with respect to input power for signal\ powers up to many hundreds of fW (≈10^{3} circulating photons), and the direction of circulation\ can be dynamically reconfigured. We demonstrate its tunability with operation at a selection\ of frequencies between 4 and 6 GHz. Given the current status of quantum error-correction and\ architectures for quantum information processing with superconducting circuits, such scalable nonreciprocal\ devices will almost certainly be necessary for construction of a superconducting quantum\ computer intended to be more than a proof-of-principle.

This thesis develops theory for and experimentally demonstrates a new way to break Lorentz\ reciprocity\textendash\textendashthe symmetry, in an electrical network, under exchange of source and detector. The\ approach is based on the sequential application of frequency conversion and delay; as frequency\ and time are Fourier duals, these operations do not generally commute. We apply this method in\ the construction of an on-chip superconducting microwave circulator, a critical component for the\ unidirectional routing of quantum information in superconducting networks. The device requires\ neither permanent magnets nor microwave control tones, allowing on-chip integration with other\ superconducting circuits without expensive control hardware. Isolation in the device exceeds 20\ dB over a bandwidth of tens of MHz, and its insertion loss is small, reaching as low as 0.9 dB at\ select operation frequencies. Furthermore, the device is linear with respect to input power for signal\ powers up to many hundreds of fW (≈10^{3} circulating photons), and the direction of circulation\ can be dynamically reconfigured. We demonstrate its tunability with operation at a selection\ of frequencies between 4 and 6 GHz. Given the current status of quantum error-correction and\ architectures for quantum information processing with superconducting circuits, such scalable nonreciprocal\ devices will almost certainly be necessary for construction of a superconducting quantum\ computer intended to be more than a proof-of-principle.