  High-gain amplifiers of electromagnetic signals operating near the quantum
limit are crucial for quantum information systems and ultrasensitive quantum
measurements. However, the existing techniques have a limited gain-bandwidth
product and only operate with weak input signals. Here we demonstrate a
two-port optomechanical scheme for amplification and routing of microwave
signals, a system that simultaneously performs high-gain amplification and
frequency conversion in the quantum regime. Our amplifier, implemented in a
two-cavity microwave optomechanical device, shows 41 dB of gain and has a high
dynamic range, handling input signals up to $10^{13}$ photons per second, three
orders of magnitude more than corresponding Josephson parametric amplifiers. We
show that although the active medium, the mechanical resonator, is at a high
temperature far from the quantum limit, only 4.6 quanta of noise is added to
the input signal. Our method can be readily applied to a wide variety of
optomechanical systems, including hybrid optical-microwave systems, creating a
universal hub for signals at the quantum level.
