  We find that feedback control may induce "pseudo" nonlinear dynamics in a
damped harmonic oscillator, whose centroid trajectory in the phase space
behaves like a classical nonlinear system. Thus, similar to nonlinear
amplifiers (e.g., rf-driven Josephson junctions), feedback control on the
harmonic oscillator can induce nonlinear bifurcation, which can be used to
amplify small signals and further to measure quantum states of qubits. Using
the circuit QED systems as an example, we show how to apply our method to
measure superconducting charge qubits.
