  We study the implementation of quantum state transfer protocols in phonon
networks, where in analogy to optical networks, quantum information is
transmitted through propagating phonons in extended mechanical resonator arrays
or phonon waveguides. We describe how the problem of a non-vanishing thermal
occupation of the phononic quantum channel can be overcome by implementing
optomechanical multi- and continuous mode cooling schemes to create a 'cold'
frequency window for transmitting quantum states. In addition, we discuss the
implementation of phonon circulators and switchable phonon routers, which rely
on strong coherent optomechanical interactions only, and do not require strong
magnetic fields or specific materials. Both techniques can be applied and
adapted to various physical implementations, where phonons coupled to spin or
charge based qubits are used for on-chip networking applications.

Quantum Physics;Mesoscale and Nanoscale Physics