Mechanically induced two-qubit gates and maximally entangled states for single electron spins in a carbon nanotube

We theoretically analyze a system where two electrons are trapped separately in two quantum dots on a suspended carbon nanotube (CNT), subject to external ac electric driving. An indirect mechanically induced coupling of two distant single electron spins is induced by the interaction between the spins and the mechanical motion of the CNT. We show that a two-qubit iSWAP gate and arbitrary single-qubit gates can be obtained from the intrinsic spin-orbit coupling. Combining the iSWAP gate and single-qubit gates, maximally entangled states of two spins can be generated in a single step by varying the frequency and the strength of the external electric driving field. The spin-phonon coupling can be turned off by electrostatically shifting the electron wave function on the nanotube.