  We propose and analyse an efficient scheme for simulating higher-order
topological phases of matter in two dimensional (2D) spin-phononic crystal
networks. We show that, through a specially designed periodic driving, one can
selectively control and enhance the bipartite silicon-vacancy (SiV) center
arrays, so as to obtain the chiral symmetry-protected spin-spin couplings. More
importantly, the Floquet engineering spin-spin interactions support rich
quantum phases associated with topological invariants. In momentum space, we
analyze and simulate the topological nontrivial properties of the one- and
two-dimensional system, and show that higher-order topological phases can be
achieved under the appropriate periodic driving parameters. As an application
in quantum information processing, we study the robust quantum state transfer
via topologically protected edge states. This work opens up new prospects for
studying quantum acoustic, and offers an experimentally feasible platform for
the study of higher-order topological phases of matter.
