Long-distance entanglement of soliton spin qubits in gated nanowires

We investigate numerically the charge, spin, and entanglement dynamics of two electrons confined in a gated semiconductor nanowire. The electrostatic coupling between electrons in the nanowire and the induced charge on the metal electrodes leads to a self-trapping of the electrons, which results in solitonlike properties. We show that the interplay of an all-electrically controlled coherent transport of the electron solitons and of the exchange interaction can be used to realize ultrafast SWAP and entangling root SWAP gates for distant spin qubits. We demonstrate that the latter gate can be used to generate a maximally entangled spin state of spatially separated electrons. The results are obtained by quantum-mechanical time-dependent calculations with exact inclusion of electron-electron correlations.