Exponentially Improved Dispersive Qubit Readout with Squeezed Light

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.