Dispersive qubit measurement using an on-chip parametric amplifier: theory

Superconducting circuits directly integrating qubits and parametric amplifiers are a promising avenue for scalable measurement in circuit QED architectures. In such devices, the qubit is not protected against the amplified fluctuations of the paramp; understanding the backaction characteristics is thus crucial. We dicuss recent theory work examining measurement-induced dephasing in a system where a flux-pumped paramp is directly coupled to a qubit, both in the limit of weak and strong dispersive coupling. We show that by careful design choices, the measurement-induced dephasing can be near quantum-limited despite the lack of circulators or explicitly directional amplifiers to protect the qubit. This work is supported by ARO.