  Josephson parametric amplifiers (JPAs) approaching quantum-limited noise
performance have been instrumental in enabling high fidelity readout of
superconducting qubits and, recently, semiconductor quantum dots (QDs). We
propose that the quantum capacitance arising in electronic two-level systems
(the dual of Josephson inductance) can provide an alternative dissipation-less
non-linear element for parametric amplification. We experimentally demonstrate
phase-sensitive parametric amplification using a QD-reservoir electron
transition in a CMOS nanowire split-gate transistor embedded in a 1.8~GHz
superconducting lumped-element microwave cavity, achieving parametric gains of
-3 to +3 dB, limited by Sisyphus dissipation. Using a semi-classical model, we
find an optimised design within current technological capabilities could
achieve gains and bandwidths comparable to JPAs, while providing complementary
specifications with respect to integration in semiconductor platforms or
operation at higher magnetic fields.
