We discuss characterization of experimental quantum gates by the error
matrix, which is similar to the standard process matrix χ in the Pauli
basis, except the desired unitary operation is factored out, by formally
placing it either before or after the error process. The error matrix has only
one large element, which is equal to the process fidelity, while other elements
are small and indicate imperfections. The imaginary parts of the elements along
the left column and/or top row directly indicate the unitary imperfection and
can be used to find the needed correction. We discuss a relatively simple way
to calculate the error matrix for a composition of quantum gates. Similarly, it
is rather straightforward to find the first-order contribution to the error
matrix due to the Lindblad-form decoherence. We also discuss a way to identify
and subtract the tomography procedure errors due to imperfect state preparation
and measurement. In appendices we consider several simple examples of the
process tomography and also discuss an intuitive physical interpretation of the
Lindblad-form decoherence.Comment: 21 pages (slightly revised version
