A quantum-limited amplifier (QLA) is a special kind of low-noise microwave amplifier with the ability to read out quantum states with high fidelity in real time.
These microwave amplifiers are quantum-limited because they add only the minimum amount of noise required by quantum mechanics to the input signal, which equals to the ambient quantum noise, i.e., a half of a photon at the signal frequency. This means that in the ideal case, the signal-to-noise ratio at the output of the QLA is only degraded by a factor of two (since the added noise and input noise are equal).
Another advantage of using these ultra-low noise amplifiers as first-stage amplifiers is that the signal-to-noise ratio of the whole amplification chain is, to a large extent, preserved following the first stage (see the bottom illustration of the qubit readout in figure 2). This is due to the helpful fact that the noise performance of a cascade of microwave amplifiers is primarily set by the noise characteristics of the first amplification stage (given it provides enough power gain).
(IBM Source)