  Quantum entanglement is one of the most important resources in quantum
information. In recent years, the research of quantum entanglement mainly
focused on the increase in the number of entangled qubits or the
high-dimensional entanglement of two particles. Compared with qubit states,
multipartite high-dimensional entangled states have beneficial properties and
are powerful for constructing quantum networks. However, there are few studies
on multipartite high-dimensional quantum entanglement due to the difficulty of
creating such states. In this paper, we experimentally prepared a multipartite
high-dimensional state
$|\Psi_{442}\rangle=\frac{1}{2}(|000\rangle+|110\rangle+|221\rangle+|331\rangle)$
by using the path mode of photons. We obtain the fidelity $F=0.854\pm0.007$ of
the quantum state, which proves a real multipartite high-dimensional entangled
state. Finally, we use this quantum state to demonstrate a layered quantum
network in principle. Our work highlights another route towards complex quantum
networks.
