A laser generates light through stimulated emission of radiation and requires population inversion. Quantum interference can yield lasing without inversion. However, such phase-sensitive quantum amplification still requires some atomic population in the excited state. Here, we present a new kind of quantum amplifier based on collective superradiant emission which does not need any population in the excited state. We show that parametric resonance between the driving (e.g., infrared) field and collective superradiant oscillations of the atomic polarization can yield light amplification at high <?format ?>(e.g., XUV) frequencies. To achieve gain, one must suppress a time-dependent Stark shift caused by the driving field. The resulting superradiant amplifier is many orders of magnitude more efficient than <?format ?>the usual nonlinear multiphoton excitation and holds promise for a new kind of generator of high-frequency coherent radiation. In addition to a detailed analytical analysis, confirmed by numerical simulations, we provide a physically appealing explanation of the quantum amplification by superradiant emission of radiation (QASER) operation in terms of coupled classical oscillators. We also present an experiment that demonstrates the QASER amplification mechanism in an electronic circuit, which, to the best of our knowledge, is the first experimental demonstration of the difference combination resonance.