  Surface acoustic waves are commonly used in classical electronics
applications, and their use in quantum systems is beginning to be explored, as
evidenced by recent experiments using acoustic Fabry-P\'erot resonators. Here
we explore their use for quantum communication, where we demonstrate a
single-phonon surface acoustic wave transmission line, which links two
physically-separated qubit nodes. Each node comprises a microwave phonon
transducer, an externally-controlled superconducting variable coupler, and a
superconducting qubit. Using this system, precisely-shaped individual itinerant
phonons are used to coherently transfer quantum information between the two
physically-distinct quantum nodes, enabling the high-fidelity node-to-node
transfer of quantum states as well as the generation of a two-node Bell state.
We further explore the dispersive interactions between an itinerant phonon
emitted from one node and interacting with the superconducting qubit in the
remote node. The observed interactions between the phonon and the remote qubit
promise future quantum optics-style experiments with itinerant phonons.
