Figure 1

(a) A complete graph with 7 nodes, with the target node in red. (b) Line with two nodes representing the reduced Hamiltonian of the complete graph with N nodes (see Eq. (13)), The solution node is represented in red and the other node represents the equal superposition of all nodes except . E₁ and E₂ represent their respective site energies and V the coupling between them. (c) The search Hamiltonian in the reduced picture (see Eq. (15)). In contrast to Fig. 1b, the site energies of both the nodes are equal, leading to perfect transport between them. Also, the transport time is given by the inverse of the coupling, which yields the running time of the algorithm .