Quantum walk of two particles on the graphene structure graph with interaction

Abstract

In this paper, we discuss the quantum walk of two interacting particles on graphene structure graph. Based on the localized graphene structure graph, we get three cases for the position of the two particles, that is ∂(i, j) = 0, ∂(i, j) = 1, and ∂(i, j) = 2. Subsequently, we investigate the quantum walk of two interacting particles from a new perspective, namely, based on the view of quantum probability, a localized quantum decomposition was used to get the corresponding creation operators and annihilation operators for the first time. Finally, we get the Hamiltonian and the time evolution operator of two interacting particles on the graphene structure graph.