  With sub-threshold quantum error correction on quantum hardware still out of
reach, quantum error mitigation methods are currently deemed an attractive
option for implementing certain applications on near-term noisy quantum
devices. One such application is quantum routing - the ability to map an
incoming quantum signal into a superposition of paths. In this work, we use a
7-qubit IBM quantum device to experimentally deploy two promising quantum error
mitigation methods, Zero-Noise Extrapolation (ZNE) and Probabilistic Error
Cancellation (PEC), in the context of quantum routing. Importantly, beyond
investigating the improved performance of quantum routing via ZNE and PEC
separately, we also investigate the routing performance provided by the
concatenation of these two error-mitigation methods. Our experimental results
demonstrate that such concatenation leads a very significant performance
improvement relative to implementation with no error mitigation. Indeed, an
almost perfect performance in terms of fidelity of the output entangled paths
is found. These new results reveal that with concatenated quantum
error-mitigation embedded, useful quantum routing becomes feasible on current
devices without the need for quantum error correction - opening up a potential
implementation pathway to other applications that utilize a superposition of
communication links.
