  Accurate detection of quantum states is a vital step in the development of
quantum computing. Image-charge detection of quantum states of electrons on
liquid helium can potentially be used for the readout of a single-electron
qubit; however, low sensitivity due to added noise hinders its usage in high
fidelity and bandwidth (BW) applications. One method to improve the readout
accuracy and bandwidth is to use cryogenic amplifications near the signal
source to minimize the effects of stray capacitance. We experimentally
demonstrate a two-stage amplification scheme with a low power dissipation of 90
{\mu}W at the first stage located at the still plate of the dilution
refrigerator and a high gain of 40 dB at the second stage located at the 4 K
plate. The good impedance matching between different stages and output devices
ensure high BW and constant gain in a wide frequency range. The detected
image-charge signals are compared for one-stage and two-stage amplification
schemes.
