  Practical quantum networks require low-loss and noise-resilient optical
interconnects as well as non-Gaussian resources for entanglement distillation
and distributed quantum computation. The latter could be provided by
superconducting circuits but - despite growing efforts and rapid progress -
existing solutions to interface the microwave and optical domains lack either
scalability or efficiency, and in most cases the conversion noise is not known.
In this work we utilize the unique opportunities of silicon photonics, cavity
optomechanics and superconducting circuits to demonstrate a fully integrated,
coherent transducer connecting the microwave X and the telecom S bands with a
total (internal) bidirectional transduction efficiency of 1.2% (135 %) at
millikelvin temperatures. The coupling relies solely on the radiation pressure
interaction mediated by the femtometer-scale motion of two silicon nanobeams
and includes an optomechanical gain of about 20 dB. The chip-scale device is
fabricated from CMOS compatible materials and achieves a V$_\pi$ as low as 16
$\mu$V for sub-nanowatt pump powers. Such power-efficient, ultra-sensitive and
highly integrated hybrid interconnects might find applications ranging from
quantum communication and RF receivers to magnetic resonance imaging.
