  We report on a quantum interface linking a diamond NV center quantum network
node and 795nm photonic time-bin qubits compatible with Thulium and Rubidium
quantum memories. The interface makes use of two-stage low-noise quantum
frequency conversion and waveform shaping to match temporal and spectral photon
profiles. Two-photon quantum interference shows high indistinguishability of
(89.5 $\pm$ 1.9)% between converted 795nm photons and the native NV center
photons. We use the interface to demonstrate quantum teleportation including
real-time feedforward from an unbiased set of 795nm photonic qubit input states
to the NV center spin qubit, achieving a teleportation fidelity of (75.5 $\pm$
1.0)%. This proof-of-concept experiment shows the feasibility of
interconnecting different quantum network hardware.
