  We define an adaptive routing method for the management of quantum memory
failures in the quantum Internet. In the quantum Internet, the entangled
quantum states are stored in the local quantum memories of the quantum nodes. A
quantum memory failure in a particular quantum node can destroy several
entangled connections in the entangled network. A quantum memory failure event
makes the immediate and efficient determination of shortest replacement paths
an emerging issue in a quantum Internet scenario. The replacement paths omit
those nodes that are affected by the quantum memory failure to provide a
seamless network transmission. In the proposed solution, the shortest paths are
determined by a base-graph, which contains all information about the overlay
quantum network. The method provides efficient adaptive routing in quantum
memory failure scenarios of the quantum Internet. The results can be
straightforwardly applied in practical quantum networks, including
long-distance quantum communications.
