  Quantum walks have been very successful in the development of search
algorithms in quantum information, in particular in the development of spatial
search algorithms. However, the construction of continuous-time quantum search
algorithms in two-dimensional lattices has proved difficult, requiring
additional degrees of freedom. Here, we demonstrate that continuous-time
quantum walk search is possible in two-dimensions by changing the search
topology to a graphene lattice, utilising the Dirac point in the energy
spectrum. This is made possible by making a change to standard methods of
marking a particular site in the lattice. Various ways of marking a site are
shown to result in successful search protocols. We further establish that the
search can be adapted to transfer probability amplitude across the lattice
between specific lattice sites thus establishing a line of communication
between these sites.
