  An optical network of superconducting quantum bits (qubits) is an appealing
platform for quantum communication and distributed quantum computing, but
developing a quantum-compatible link between the microwave and optical domains
remains an outstanding challenge. Operating at $T < 100$ mK temperatures, as
required for quantum electrical circuits, we demonstrate a
mechanically-mediated microwave-optical converter with 47$\%$ conversion
efficiency, and use a feedforward protocol to reduce added noise to 38 photons.
The feedforward protocol harnesses our discovery that noise emitted from the
two converter output ports is strongly correlated because both outputs record
thermal motion of the same mechanical mode. We also discuss a quantum
feedforward protocol that, given high system efficiencies, allows quantum
information to be transferred even when thermal phonons enter the mechanical
element faster than the electro-optic conversion rate.
