  Modern computing and communication technologies such as supercomputers and
the internet are based on optically connected networks of microwave frequency
information processors. In recent years, an analogous architecture has emerged
for quantum networks with optically distributed entanglement between remote
superconducting quantum processors, a leading platform for quantum computing.
Here we report an important milestone towards such networks by observing
non-classical correlations between photons in an optical link and a
superconducting electrical circuit. We generate such states of light through a
spontaneous parametric down-conversion (SPDC) process in a chip-scale
piezo-optomechanical transducer. The non-classical nature of the emitted light
is verified by observing anti-bunching in the microwave state conditioned on
detection of an optical photon. Such a transducer can be readily connected to a
superconducting quantum processor, and serve as a key building block for
optical quantum networks of microwave frequency qubits.
