Coupling Distant Spins of Surface-State Electrons by Manipulating Their Collective Vibrations

The system of electrons on liquid helium is an interesting candidate to implement quantum computation,due to the long coherence times of the qubits encoded by the electronic spins.In order to implement the quantum logic operations between the spins,we propose here a configuration,similarly to the cooled ions in a trap,to couple the distant electrons via manipulating their center of mass(CM)vibrations.First,we show that the electrons could be confined in a common harmonic oscillator potential by using an electrostatic field.Then,with a single current pulse(applied on the micro-electrode below the liquid helium) the distant electronic spins can be coupled simultaneously to the CM mode.Finally,by adiabatically eliminating the CM mode,efective interaction between the distant spins is induced for implementing the desired quantum computing.