Double quantum dot of graphene nanoribbon qubit for Quantum information

Weak hyperfine interaction as well as spin-orbit interaction enforced that graphene quantum dot qubit material rather than other semiconductor qubits material. So; we suggest here a Hamiltonian model of a graphene nanoribbon double quantum dot qubit based on the functionalization of graphene nanoribbon by hydrogen atoms to produce a theoretical studied on a quantum computer. We are using the Dirac equation and the Heisenberg exchange approach to solve our model. Then we determine the exchange interaction Jex. We investigate the effects of potential barrier height and barrier thickness d on exchange coupling Jex. Our results show a great variation of Jex depends on these parameters, and how this parameter affected on Jex at special value. Also, we can use the variation of Jex with both potential barrier height and barrier thickness d to represent how the information can transfer, which is important to gate operation necessary for quantum information.