  We demonstrate the first solid-state spin-wave optical quantum memory with
on-demand read-out. Using the full atomic frequency comb scheme in a \PrYSO
crystal, we store weak coherent pulses at the single-photon level with a signal
to noise ratio $> 10$. Narrow-band spectral filtering based on spectral hole
burning in a second \PrYSO crystal is used to filter out the excess noise
created by control pulses to reach an unconditional noise level of $(2.0 \pm
0.3) \times10^{-3}$ photons per pulse. We also report spin-wave storage of
photonic time-bin qubits with conditional fidelities higher than a measure and
prepare strategy, demonstrating that the spin-wave memory operates in the
quantum regime. This makes our device the first demonstration of a quantum
memory for time-bin qubits, with on demand read-out of the stored quantum
information. These results represent an important step for the use of
solid-state quantum memories in scalable quantum networks.
