@ekert_quantum_1991; @cirac_distributed_1999; @Dur_entanglement_2003]. Propagating optical fields are the natural choice for quantum links in such a network, as they enable entanglement distribution at room temperature and over kilometer-scale distances. The fast-paced development of superconducting quantum processors [@kelly_state_2015; @ofek_extending_2016] suggests that the most powerful nodes will use microwave-frequency excitations in ultralow-temperature environments ($T<100~\text{mK}$), implying that a quantum state preserving electro-optic converter is a crucial element needed for a future quantum internet. Prospective conversion technologies under investigation are ultracold atoms [@verdu_strong_2009; @hafezi_atomic_2012], optically active spins in solids [@imamoglu_cavity_2009; @marcos_coupling_2010; @kubo_strong_2010; @williamson_magneto-optic_2014], magnons [@hisatomi_bidirectional_2016], electro-optic materials [@ilchenko_whispering-gallery-mode_2003; @xiong_low-loss_2012; @rueda_efficient_2016], and mechanical resonators [@bochmann_nanomechanical_2013; @andrews_bidirectional_2014; @vainsencher_bi-directional_2016]. To date there has been no successful demonstration of an electro-optic converter capable of quantum operation. Recent realizations have demonstrated improved capacity for classical signal recovery, albeit at elevated operating temperatures[@andrews_bidirectional_2014; @bochmann_nanomechanical_2013; @bagci_optical_2014; @vainsencher_bi-directional_2016; @takeda_electro-mechano-optical_2018].

Realizing a quantum electro-optic converter is a challenging task because it entails bringing together superconducting quantum circuits and laser light in an ultralow-temperature environment. The potential for quantum operation can be delineated via two metrics: the bidirectional efficiency between the microwave and optical ports, and the added noise of the converter $N_{\mathrm{add}}$ [@safavi-naeini_proposal_2011; @hill_coherent_2012; @andrews_bidirectional_2014; @zeuthen_figures_2016]. In a mechanical converter, low added noise 