  We demonstrate a radio-frequency parametric amplifier that exploits the
gate-tunable quantum capacitance of an ultra high mobility two dimensional
electron gas (2DEG) in a GaAs heterostructure at cryogenic temperatures. The
prototype narrowband amplifier exhibits a gain greater than 20 dB up to an
input power of - 66 dBm (1 dB compression), and a noise temperature TN of 1.3 K
at 370 MHz. In contrast to superconducting amplifiers, the quantum capacitance
parametric amplifier (QCPA) is operable at tesla-scale magnetic fields and
temperatures ranging from milli kelvin to a few kelvin. These attributes,
together with its low power (microwatt) operation when compared to conventional
transistor amplifiers, suggest the QCPA may find utility in enabling on-chip
integrated readout circuits for semiconductor qubits or in the context of space
transceivers and radio astronomy instruments.
