  We propose a device architecture capable of direct quantum electro-optical
conversion of microwave to optical photons. The hybrid system consists of a
planar superconducting microwave circuit coupled to an integrated
whispering-gallery-mode microresonator made from an electro-optical material.
We show that electro-optical (vacuum) coupling rates $g_0$ as large as$\sim
2\pi \, \mathcal{O}(10-100)$ kHz are achievable with currently available
technology, due to the small mode volume of the planar microwave resonator.
Operating at millikelvin temperatures, such a converter would enable
high-efficiency conversion of microwave to optical photons. We analyze the
added noise, and show that maximum conversion efficiency is achieved for a
multi-photon cooperativity of unity which can be reached with optical power as
low as $ \mathcal{O}(1)\,\mathrm{mW} $.
