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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.