  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 Nd$^{3+}$:Y$_2$SiO$_5$ (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
$^{145}$Nd nuclear spin states in Nd$^{3+}$:YSO. We find nuclear spin coherence
times can reach 9 ms at $\approx 5$ K, about two orders of magnitude longer
than the electron spin coherence, while quantum state and process tomography of
the storage/retrieval operation 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.
