Graphene-enabled low-control quantum gates between static and mobile spins

We show that the features of Klein tunneling make graphene a unique interface for implementing low control quantum gates between static and mobile qubits. A ballistic electron spin is considered as the mobile qubit, while the static qubit is the electronic spin of a quantum dot fixed in a graphene nanoribbon. Scattering is the low control mechanism of the gate, which in other systems is very difficult to exploit because of both backscattering and the momentum dependence of transmission. We find that the unique features of Klein tunneling enable quasideterministic quantum gates between the spin of a ballistic electron and a static spin held in a dot, regardless of the momenta or the shape of the incident electron wave function. The Dirac equation is used to describe the system in the one particle approximation, with the interaction between the static and the mobile spins modeled by a Heisenberg Hamiltonian. Furthermore, we discuss an application of this model to generate entanglement between two well-separated static qubits.