Transformed dissipation in superconducting quantum circuits

Superconducting quantum circuits must be designed carefully to avoid dissipation from coupling to external control circuitry. We describe a reformulation of dissipation theory based on a current-to-current transformer model. We test this theory with an experimentally determined impedance transformation of 105 and find quantitative agreement better than a factor of 2 between this transformation and the reduced lifetime of a phase qubit coupled to a tunable transformer. Higher-order corrections from quantum fluctuations are also calculated with this theory, but found not to limit the qubit lifetime. We also illustrate how this simple connection between current and impedance transformation can be used to rule out dissipation sources in experimental qubit systems.