  We have investigated the realizability of the controlled-NOT (CNOT) gate and
characterized the gate operation by quantum process tomography for a chain of
qubits, realized by electrons confined in self-assembled quantum dots embedded
in the spin field-effect transistor. We have shown that the CNOT gate operation
and its process tomography are performable by using the spin exchange
interaction and several local qubit rotations within the coherence time of
qubits. Moreover it is shown that when the fluctuation of operation time and
the imperfection of polarization of channel electrons are considered as sources
of decay of fidelity, the process fidelity of CNOT decreases at most 5% by the
fluctuation of the operation time and its values of 0.49 and 0.72 are obtained
for polarizations of the channel spin 0.6 and 0.8, respectively.
