Qubits and gate operations in a topologically protected system of a toroidal flux coupled to an electron

We study a model of quantized toroidal magnetic flux coupled to a charged particle through field-free interaction. We solve this model and show that the topological and nonlocal aspects of this Aharonov-Bohm-like system can have profound applications in quantum information. We show how these flux qubits are protected from the environmental noise, and how to do nonlocal operations on them including creating entanglement between them.