  We report on the high-efficiency storage and retrieval of weak coherent
optical pulses and photonic qubits in a cavity-enhanced solid-state quantum
memory. By using an atomic frequency comb (AFC) memory in a $Pr^{3+}:Y_2 SO_5$
crystal embedded in a low-finesse impedance-matched cavity, we stored weak
coherent pulses at the single photon level with up to 62% efficiency for a
pre-determined storage time of 2 $\mu$s. We also confirmed that the
impedance-matched cavity enhances the efficiency for longer storage times up to
70 $\mu$s. Taking advantage of the temporal multimodality of the AFC scheme, we
then store weak coherent time-bin qubits with (51+-2)% efficiency and a
measurement-device limited fidelity over (94.8+-1.4)% for the retrieved qubits.
These results represent the most efficient storage in a single photon level AFC
memory and the most efficient qubit storage in a solid-state quantum memory
up-to-date.
