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Interfacing between various elements of a computer-from memory to processors to long range communication-will be as critical for quantum computers as it is for classical computers today. Paramagnetic rare-earth doped crystals, such as Nd3+: Y2SiO5(YSO), are excellent candidates for such a quantum interface: they are known to exhibit long optical coherence lifetimes (for communication via optical photons), possess a nuclear spin (memory), and have in addition an electron spin that can offer hybrid coupling with superconducting qubits (processing). Here we study two of these three elements, demonstrating coherent storage and retrieval between electron and 145Nd nuclear spin states in Nd3+: YSO. We find nuclear spin coherence times can reach 9 ms at ~5 K, about 2 orders of magnitude longer than the electron spin coherence, while quantum state and process tomography of the storage or retrieval operation between the electron and nuclear spin reveal an average state fidelity of 0.86. The times and fidelities are expected to further improve at lower temperatures and with more homogeneous radio-frequency excitation. [ABSTRACT FROM AUTHOR]