Potential Errors in a Scheme of Universal Quantum Gates in Kane's Model

We re--investigate a plausible proposal for universal quantum gates in Kane's model, in which the authors assumed that electron spin is always downward under a background magnetic field and the value of controlling parameters is varied instantaneously. We demonstrate that a considerable error appears, for example, in the X rotation. As result, the controlled operations don't work. Such a failure is caused by improper choice of the computational bases; actually, the electron spin is not always downward over time during quantum operations.