  It has been a long-standing goal to improve dispersive qubit readout with
squeezed light. However, injected external squeezing (IES) {\it cannot} enable
a practically interesting increase in the signal-to-noise ratio (SNR), and
simultaneously, the increase of the SNR due to the use of intracavity squeezing
(ICS) is even {\it negligible}. Here, we {\it counterintuitively} demonstrate
that using IES and ICS together can lead to an {\it exponential} improvement of
the SNR for any measurement time, corresponding to a measurement error reduced
typically by many orders of magnitude. More remarkably, we find that in a
short-time measurement, the SNR is even improved exponentially with {\it twice}
the squeezing parameter. As a result, we predict a fast and high-fidelity
readout. This work offers a promising path toward exploring squeezed light for
dispersive qubit readout, with immediate applications in quantum error
correction and fault-tolerant quantum computation.
