  In the present paper methods and algorithms of modeling quantum operations
for quantum computer integrated circuits design are developed. We examine
different ways of quantum operation descriptions, including operator-sums,
unitary representations, Choi-Jamiolkowski state representations and the
corresponding chi-matrices, as well as quantum system evolution operators. The
results of modeling of practically important quantum gates: SQiSW (square root
of i-SWAP gate), controlled-NOT (CNOT), and controlled Z-transform (CZ) subject
to different decoherence mechanisms are presented. These mechanisms include
analysis of depolarizing quantum noise and processes of amplitude and phase
relaxation. Finally, we consider error correction of phase flip, and the tasks
of creating and maintaining the entanglement, as well as its breaking for two-
and multi-qubit realizations of quantum operations. Importance of the present
analysis for the quality and efficiency of quantum information technologies in
practical applications is discussed.
