  Here we demonstrate quantum teleportation through hypergraph states, which
are the generalization of graph states, and due to their non-local entanglement
properties, it allows us to perform quantum teleportation. Here we design some
hypergraph states useful for quantum teleportation and process the schemes for
quantum teleportation of single-qubit and two-qubit arbitrary states via
three-uniform three-qubit and four-qubit hypergraph states respectively. We
explicate the experimental realization of quantum teleportation of both single
and two-qubit arbitrary states. Then we run our quantum circuits on the IBM
quantum experience platform, where we present the results obtained by both the
simulator and real devices such as "ibmq_qasm_simulator" and
"ibmq_16_melbourne" and calculate the fidelity. We observe that the real device
has some errors in comparison to the simulator, these errors are due to the
decoherence effect in the quantum channel and gate errors. We then illustrate
the experimental and theoretical density matrices of teleported single and
two-qubit states.
