  In quantum networks an important goal is to reduce resource requirements for
the transport and communication of quantum information. Quantum network coding
presents a way of doing this by distributing entangled states over a network
that would ordinarily exhibit contention. In this work, we study
measurement-based quantum network coding (MQNC), which is a protocol
particularly suitable for noisy intermediate-scale quantum devices. MQNC has
previously been studied experimentally on a superconducting processor, however
the resulting states did not have a usable degree of entanglement. We adapt
MQNC to the newer superconducting processor ibm_cairo and obtain a much
improved degree of entanglement, enabling us to demonstrate successful
teleportation of quantum information. The teleportation is shown to occur with
fidelity higher than could be achieved via classical means, made possible by
considering qubits from a polar cap of the Bloch Sphere. We also present a
generalization of MQNC with a simple mapping onto the heavy-hex processor
layout and a direct mapping onto a proposed logical error-corrected layout. Our
work provides some useful techniques for testing and successfully carrying out
quantum network coding.
