  We propose a novel hybrid platform where solid-state spin qubits are coupled
to the acoustic modes of a two-dimensional array of optomechanical nano
cavities. Previous studies of coupled optomechanical cavities have shown that
in the presence of strong optical driving fields, the interplay between the
photon-phonon interaction and their respective inter-cavity hopping allows the
generation of topological phases of sound and light. In particular, the
mechanical modes can enter a Chern insulator phase where the time-reversal
symmetry is broken. In this context, we exploit the robust acoustic edge states
as a chiral phononic waveguide and describe a state transfer protocol between
spin qubits located in distant cavities. We analyze the performance of this
protocol as a function of the relevant system parameters and show that a
high-fidelity and purely unidirectional quantum state transfer can be
implemented under experimentally realistic conditions. As a specific example,
we discuss the implementation of such topological quantum networks in diamond
based optomechanical crystals where point defects such as silicon-vacancy
centers couple to the chiral acoustic channel via strain.
