  Classical Floyd-Warshall algorithm is used to solve all-pairs shortest path
problem on a directed graph. The classical algorithm runs in \mathcal{O}
(V^{3}) time where V represents the number of nodes. Here we have modified the
algorithm and proposed a quantum algorithm analogous to Floyd-Warshall
algorithm which exploits the superposition principle and runs in \mathcal{O}
(Vlog_{2}V) time.
