Systematic Design of Microwave Parametric Amplifiers, Frequency Converters, and Circulators

The success of Josephson parametric amplifiers in enabling high-fidelity readout of superconducting qubits has led to a flurry of research into parametrically-coupled networks, including amplifiers, frequency converters, and parametric non-reciprocal networks. Despite significant progress, the lack of a design methodology to allow engineering their transfer characteristics — gain, ripple, bandwidth, isolation — means that their bandwidth remains limited (in most cases ~10s of MHz), their performance remains hard to predict, and their design remains the purview of advanced physics degree holders. In this talk we will show how band-pass impedance matching and filter network synthesis techniques from microwave engineering can be applied to the design of Josephson parametric and non-reciprocal devices. We will briefly review the physics of parametrically-coupled networks, show that parametric couplings function analogously to immittance inverters in microwave circuits, and then apply filter synthesis techniques to design a range of reference parametrically-coupled circuits. We demonstrate via simulation that by use of these established microwave engineering techniques it is possible to dramatically simplify the design of wideband Josephson parametric amplifiers, frequency converters, and circulators. Our work also opens the door for microwave engineers and filter designers to have a significant impact on a key subsystem in quantum processor readout.