  The requirements and details of designing a measuring cell and
low-back-action deeply-cooled amplifier for quantum measurements at 10 mK are
discussed. This equipment is a part of a microwave single-photon counter based
on a superconducting flux qubit. The high electron mobility transistors (HEMTs)
in the amplifier operate in unsaturated microcurrent regime and dissipate only
1 microwatt of dc power per transistor. Simulated amplifier gain is 15 dB at
450 MHz with a high-impedance (~5 kOhm signal source and standard 50-Ohm
output.
