similar measurement setup, one would expect feedforward performance similar to that observed here, but laser cooling to be orders of magnitude less effective.

Looking ahead to quantum feedforward operation, a central challenge is improving microwave and optical measurement performance. In particular the microwave measurement noise could be improved by using a quantum-limited microwave amplifier [@teufel_nanomechanical_2009]. Meanwhile, more theoretical work is needed to thoroughly explore the electro-optomechanical correlations identified here, and to study optimal qubit encodings for microwave-optical conversion with feedforward.

Methods {#methods .unnumbered}
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### Device parameters {#device-parameters .unnumbered}

We realize an electro-optic converter by simultaneously coupling microwave and optical resonators to a single mode of a mechanical oscillator. The mechanical oscillator is a thin, suspended dielectric membrane, with resonant frequency $\omega_\mathrm{m} / 2 \pi = f_\mathrm{m} = 1.473~\mathrm{MHz}$ for the mode of interest. A portion of the membrane is metallized and arranged as a mechanically compliant capacitor in a superconducting LC circuit, with resonant frequency $\omega_\mathrm{e}/2\pi = 6.16~\mathrm{GHz}$ and linewidth $\kappa_\mathrm{e} = 2 \pi \times 2.5~\mathrm{MHz}$. Another portion of the membrane is situated in the mode of a Fabry-Perot optical cavity with resonant frequency $\omega_\mathrm{o}/2\pi = 281.8~\mathrm{THz}$ and linewidth $\kappa_\mathrm{o} = 2 \pi \times 2.1~\mathrm{MHz}$. Vibrational motion of the 