  Quantum routing, the entanglement of an input quantum signal over multiple
output paths, will be an important aspect of future quantum networks.
Implementation of such routing in emerging quantum networks via the noisy
quantum devices currently under development is a distinct possibility. Quantum
error correction, suitable for the arbitrary noisy quantum channels experienced
in the routing process, will be required. In this work, we design a combined
circuit for quantum routing and quantum error correction, and carry out the
first implementation of such a circuit on a noisy real-world quantum device.
Under the assumption of statistical knowledge on the channel, we experimentally
verify the quantum nature of the error-corrected quantum routing by determining
the path-entanglement through quantum state tomography, measuring also its
probability of success. The quantum error correction deployed is identified as
successful in terms of improving the routing. Our experiments validate, for the
first time, that error-corrected quantum routing in near-term noisy
quantum-computing devices is feasible, and our detailed results provide a
quantum-routing benchmark for all near-term quantum hardware.
