A controlled-NOT gate in a chain of qubits embedded in a spin field-effect transistor and its process tomography

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 we have taken into account the fluctuation of operation time and the imperfection of polarization of channel electrons as sources of decay of fidelity. The cnot process fidelity decreases only by at most 5% by the fluctuation of the operation time and its values as high as 0.49 and 0.72 are obtained for the channel spin polarizations of 0.6 and 0.8, respectively.