  Quantum teleportation, the faithful transfer of an unknown input state onto a
remote quantum system, is a key component in long distance quantum
communication protocols and distributed quantum computing. At the same time,
high frequency nano-optomechanical systems hold great promise as nodes in a
future quantum network, operating on-chip at low-loss optical telecom
wavelengths with long mechanical lifetimes. Recent demonstrations include
entanglement between two resonators, a quantum memory and microwave to optics
transduction. Despite these successes, quantum teleportation of an optical
input state onto a long-lived optomechanical memory is an outstanding
challenge. Here we demonstrate quantum teleportation of a polarization-encoded
optical input state onto the joint state of a pair of nanomechanical
resonators. Our protocol also allows for the first time to store and retrieve
an arbitrary qubit state onto a dual-rail encoded optomechanical quantum
memory. This work demonstrates the full functionality of a single quantum
repeater node, and presents a key milestone towards applications of
optomechanical systems as quantum network nodes.
