Figure 3
(a) Complete bipartite graph K4,3 with the solution node 
, represented in red. (b) The reduced search Hamiltonian for the complete bipartite graph 
with m1 + m2 = N in the Lanczos basis. 
are the equal superposition of the nodes in partition 1 (excluding 
) and 2, respectively. However, the understanding of why the search is optimal in this graph is shown in Fig. 3c. (c) The same Hamiltonian as in Fig. 3b, after a basis rotation gives us an idea as to why the algorithm works optimally. The resultant basis is 
, 
and 
. The degeneracy between site energies of 
and 
facilitates transport between these two nodes while transport between 
and 
is inhibited by the energy gap between them (much larger than the coupling V2). Since there is a considerable overlap between the initial superposition of states 
and 
, there is a large probability amplitude at 
after a time 
.
