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In the present paper methods and algorithms of modeling quantum operationsfor quantum computer integrated circuits design are developed. We examinedifferent ways of quantum operation descriptions, including operator-sums,unitary representations, Choi-Jamiolkowski state representations and thecorresponding chi-matrices, as well as quantum system evolution operators. Theresults of modeling of practically important quantum gates: SQiSW (square rootof i-SWAP gate), controlled-NOT (CNOT), and controlled Z-transform (CZ) subjectto different decoherence mechanisms are presented. These mechanisms includeanalysis of depolarizing quantum noise and processes of amplitude and phaserelaxation. Finally, we consider error correction of phase flip, and the tasksof creating and maintaining the entanglement, as well as its breaking for two-and multi-qubit realizations of quantum operations. Importance of the presentanalysis for the quality and efficiency of quantum information technologies inpractical applications is discussed.

Mathematical modeling of quantum noise and the quality of hardware components of quantum computers