Demonstration of teleportation across a quantum network code

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. In particular, we develop techniques to adapt MQNC to state-of-the-art superconducting processors and subsequently demonstrate successful teleportation of quantum information, giving new insight into MQNC in this context after a previous study was not able to produce a useful degree of entanglement. The teleportation in our demonstration 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.