In this paper we answer the question of when circulant quantum spin networks with nearest-neighbor couplings can give perfect state transfer. The network is described by a circulant graph G, which is characterized by its circulant adjacency matrix A. Formally, we say that there exists a perfect state transfer (PST) between vertices a, b ∈ V (G) if |F (τ)ab| = 1, for some positive real number τ ...