Hybrid Integrated Photonic–Rare-Earth Quantum Memory at 4 K: Multimode Scaling and On-Chip Repeater Architectures

We present a theoretical and device-oriented analysis of a hybrid quantum memory platformcombining integrated nanophotonic waveguides with rare-earth-ion-doped crystals operating at 4 K.The architecture bridges two regimes: (i) solid-state long-lived spin coherence in Eu3+ :Y2 SiO5 andPr3+ :Y2 SiO5 , and (ii) scalable photonic routing in SiN and TFLN integrated circuits.We derive performance bounds for evanescent coupling, multimode storage capacity, and end-to-end efficiency under experimentally realistic constraints. Our results indicate that such hybridsystems can operate as compact quantum repeater nodes with ∼ 102 –103 temporal modes, whilemaintaining ms-scale spin coherence and chip-scale footprint.Beyond theoretical modeling, we discuss implementation constraints and design trade-offs relevantto near-term nanophotonic fabrication platforms.