  Motivated by the recent experimental observations [M. Kataoka et al., Phys.
Rev. Lett. {\bf102}, 156801 (2009)], we propose here an theoretical approach to
implement quantum computation with bound states of electrons in moving quantum
dots generated by the driving of surface acoustic waves. Differing from static
quantum dots defined by a series of static electrodes above the two-dimensional
electron gas (2DEG), here a single electron is captured from a 2DEG-reservoir
by a surface acoustic wave (SAW) and then trapped in a moving quantum dot (MQD)
transporting across a quasi-one dimensional channel (Q1DC), wherein all the
electrons have been excluded out by the actions of the surface gates. The
flying qubit introduced here is encoded by the two lowest adiabatic levels of
the electron in the MQD, and the Rabi oscillation between these two levels
could be implemented by applying finely-selected microwave pulses to the
surface gates. By using the Coulomb interaction between the electrons in
different moving quantum dots, we show that a desirable two-qubit operation,
i.e., i-SWAP gate, could be realized. Readouts of the present flying qubits are
also feasible with the current single-electron detected technique.
