Programmable cavity-enhanced telecom quantum memory in thin-film lithium niobate

Spectrally multiplexed telecom quantum networks require quantum memories that combine efficient storage with programmable frequency addressing. An ideal integrated implementation should therefore unite a native telecom transition, efficient storage and fast on-chip spectral control. Here we demonstrate a cavity-enhanced quantum memory in an isotopically purified $^{167}\mathrm{Er}^{3+}$-doped thin-film lithium niobate microring resonator. Long-lived hyperfine shelving states support persistent, high-contrast atomic frequency comb preparation, with a single-component comb lifetime of $277.6 \pm 52.6$s. Together with cavity impedance matching, this yields an on-chip storage efficiency of $23.3 \pm 0.5\%$ for 100-ns storage. The intrinsic electro-optic response of lithium niobate enables frequency-selective storage and routing of retrieved photons at rates up to 20~MHz with inter-channel crosstalk below $10^{-4}$. We further store and retrieve time-energy-entangled telecom photons, violating an entanglement-witness bound by more than 11 standard deviations and thus verifying the quantum nature of the storage process. Our results establish erbium-doped thin-film lithium niobate as a programmable light--matter interface for spectrally multiplexed quantum networks.