  Connecting superconducting qubits to optical fiber necessitates the
conversion of microwave photons to optical photons. Modern experimental
demonstrations exhibit strong coupling between a microwave resonator and an
optical cavity mediated through phononic modes in a mechanical oscillator. This
paradigmatic transduction experiment is bounded by a theoretical efficiency
with constant driving amplitudes on the electromagnetic resonators. By adding a
parametric drive to the microwave resonator and optical cavity we discover the
converted signal through the quantum transducer is amplified, while maintaining
a lower level of the added noise. We propose a theoretical framework for
time-dependent control of the driving lasers based on the input-output
formalism of quantum optics, and solve analytically the transduction efficiency
and added noise when the control signals parametrically drive the system. Our
results show better transduction efficiency and lower added noise in varying
parameter regimes relevant to current transduction experiments.
