Topological nonlocal operations on toroidal flux qubits

We propose a method to achieve coherent, field-free coupling between the toroidal flux qubit (tfluxon), which is isolated from the environment, and a charged particle on a quantum ring. The resulting nonlocal coupling is mediated only by the vector potential and can be used to control the tfluxon by acting on the quantum ring's degrees of freedom. Furthermore, the emergent coupling can facilitate coherent interaction between states of distant tfluxons mediated by an electron on a quantum ring. We demonstrate that the topological and nonlocal aspects of this system are of fundamental interest and can have important applications in quantum information, benefiting from the decoupling from the environment and the topological protection.