Time-resolved qubit readout via nonlinear Josephson inductance

We propose a generalization of dispersive qubit readout that provides the time evolution of a flux qubit observable. Our proposal relies on the nonlinear coupling of the qubit to a harmonic oscillator with high frequency, representing a dc superconducting quantum interference device. Information about the qubit dynamics is obtained by recording the oscillator response to resonant driving and subsequent lock-in detection. The measurement process is simulated for the example of coherent qubit oscillations. This corroborates the underlying measurement relation and also reveals that the measurement scheme possesses low backaction and high fidelity.