  Fault-tolerant spin-based quantum computers will require fast and accurate
qubit readout. This can be achieved using radio-frequency reflectometry given
sufficient sensitivity to the change in quantum capacitance associated with the
qubit states. Here, we demonstrate a 23-fold improvement in capacitance
sensitivity by supplementing a cryogenic semiconductor amplifier with a SQUID
preamplifier. The SQUID amplifier operates at a frequency near 200 MHz and
achieves a noise temperature below 600 mK when integrated into a reflectometry
circuit, which is within a factor 120 of the quantum limit. It enables a record
sensitivity to capacitance of 0.07 aF/\sqrt{Hz}. The setup is used to acquire
charge stability diagrams of a gate-defined double quantum dot in a short time
with a signal-to-noise ration of about 38 in 1 microsecond of integration time.
