Indirect hyperfine interaction between nuclear spin qubits in mesoscopic wires and rings

A theoretical study of the indirect coupling of nuclear spins (qubits) embedded in a mesoscopic ring and in a finite-length quantum wire in a magnetic field is presented. It is found that the hyperfine interaction, via the conduction electrons, between nuclear spins exhibits sharp maxima as a function of the magnetic field and nuclear spin positions. This phenomenon can be used for manipulation of qubits with almost atomic precision. Experimental feasibility and implications for quantum logic devices is discussed.