Quantum walks and quantum search on graphene lattices

TL;DR

This paper demonstrates that continuous-time quantum walk search algorithms can be effectively implemented on two-dimensional graphene lattices by leveraging the Dirac point, enabling efficient site marking and communication.

Contribution

The authors show how to adapt quantum search algorithms to 2D graphene lattices using modified site marking techniques and energy spectrum properties.

Findings

Successful quantum search protocols on graphene lattices.

Ability to transfer probability amplitude between specific sites.

Establishment of communication lines across the lattice.

Abstract

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.