  Dynamical properties of a resonator can be analyzed using the
Rayleigh-Lorentz invariant which is not an exact constant but varies more or
less over time. We investigate the time behavior of this invariant for a flux
qubit resonator in order for better understanding of qubit-information
detection with the resonator. Flux qubit resonators can be utilized in
implementing diverse next generation nano-optic and nano-electronic devices
such as quantum computing systems. Through the analyses of the temporal
evolution of the invariant, we derive a condition for optimal adiabatic
qubit-information detection with the resonator. This condition is helpful for
controlling the dynamics of qubit resonators over long periods of time. It is
necessary to consider it when designing a nano-resonator used for quantum
nondemolition readouts of qubit states, crucial in quantum computation.
