  Kronecker graphs, obtained by repeatedly performing the Kronecker product of
the adjacency matrix of an "initiator" graph with itself, have risen in
popularity in network science due to their ability to generate complex networks
with real-world properties. In this paper, we explore spatial search by
continuous-time quantum walk on Kronecker graphs. Specifically, we give
analytical proofs for quantum search on first-, second-, and third-order
Kronecker graphs with the complete graph as the initiator, showing that search
takes Grover's $O(\sqrt{N})$ time. Numerical simulations indicate that
higher-order Kronecker graphs with the complete initiator also support optimal
quantum search.
