  Transduction of quantum signals between the microwave and the optical ranges
will unlock powerful hybrid quantum systems enabling information processing
with superconducting qubits and low-noise quantum networking through optical
photons. Most microwave-to-optical quantum transducers suffer from thermal
noise due to pump absorption. We analyze the coupled thermal and wave dynamics
in electro-optic transducers that use a two-step scheme based on an
intermediate frequency state in the THz range. Our analysis, supported by
numerical simulations, shows that the two-step scheme operating with a
continuous pump offers near-unity external efficiency with a multi-order noise
suppression compared to direct transduction. As a result, two-step
electro-optic transducers may enable quantum noise-limited interfacing of
superconducting quantum processors with optical channels at MHz-scale bitrates.
