Circuit modeling of flux qubits interacting with superconducting waveguides

Abstract

We present an equivalent circuit approach to understand, simulate and design experimental setups, where superconducting coplanar resonators are applied to probe quantum systems. We employ finite-element electromagnetic simulations to construct an equivalent lumped circuit representation of the microwave cavity and we use a circuit model based on the Bloch equations to simulate the behavior of a two-state model quantum system. Interconnection of the two circuit modules gives a semiclassical description of the coupled quantum/classical dynamics and yields predictions that are directly comparable with measurements on realized circuits.