  We define the entanglement-gradient routing scheme for quantum repeater
networks. The routing framework fuses the fundamentals of swarm intelligence
and quantum Shannon theory. Swarm intelligence provides nature-inspired
solutions for problem solving. Motivated by models of social insect behavior,
the routing is performed using parallel threads to determine the shortest path
via the entanglement gradient coefficient, which describes the feasibility of
the entangled links and paths of the network. The routing metrics are derived
from the characteristics of entanglement transmission and relevant measures of
entanglement distribution in quantum networks. The method allows a moderate
complexity decentralized routing in quantum repeater networks. The results can
be applied in experimental quantum networking, future quantum Internet, and
long-distance quantum communications.
