  We observe measurement-induced qubit state mixing in a transmon qubit
dispersively coupled to a planar readout cavity. Our results indicate that
dephasing noise at the qubit-readout detuning frequency is up-converted by
readout photons to cause spurious qubit state transitions, thus limiting the
nondemolition character of the readout. Furthermore, we use the qubit
transition rate as a tool to extract an equivalent flux noise spectral density
at f ~ 1 GHz and find agreement with values extrapolated from a $1/f^\alpha$
fit to the measured flux noise spectral density below 1 Hz.
