  Quantum particles are known to be faster than classical when they propagate
stochastically on certain graphs. A time needed for a particle to reach a
target node on a distance, the hitting time, can be exponentially less for
quantum walks than for classical random walks. It is however not known how fast
would interacting quantum particles propagate on different graphs. Here we
present our results on hitting times for quantum walks of identical particles
on cycle graphs, and relate the results to our previous findings on the
usefulness of identical interacting particles in quantum information theory. We
observe that interacting fermions traverse cycle graphs faster than
non-interacting fermions. We show that the rate of propagation is related to
fermionic entanglement: interacting fermions keep traversing the cycle graph as
long as their entanglement grows. Our results demonstrate the role of
entanglement in quantum particles propagation. These results are of importance
for understanding quantum transport properties of identical particles.
