An optical network of superconducting quantum bits (qubits) is an appealing platform for quantum communication and distributed quantum computing, but developing a quantum-compatiblelink 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.[/expand]