Quantum computations results from the link between quantum mechanics, computer science and classical / quantum information theory. It uses quantum mechanical effects, especially superposition, interference and entanglement, to perform new types of computation which show promise to be more efficient than classical computations. It is the essential trait of the theory of quantum mechanics to make (exclusively) probabilistic predictions, i.e. for a quantum mechanical experiment the theory predicts possible results and their probabilities to occur. This is what makes quantum computing probabilistic.

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**176**)The article presents material for further education of students of the master's degree. In particular, the features of the application of linear algebra and the theory of matrices for the design of quan-tum algorithms are presented.

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**154**)The goal of this pedagogical article is to describe for IT engineering researchers and master course students main mathematical operations with matrices and linear operators used in quantum computing and quantum information theory. These operations are defined in the framework of linear algebra and therefore for their understanding there is no need to introduce physical background of quantum mechanics.

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**150**)Quantum mechanics requires the operations of quantum computing to be unitary, and makes it important to have general techniques for developing fast quantum algorithms for computing unitary transformations. A quantum routine for computing a generalized Kronecker product is given. Applications for computing the Walsh-Hadamard and quantum Fourier transform is include also re-development of the according network.

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**149**)The bases of quantum computation are three operators on quantum coherent states as following: superposition, entanglement and interference. The coherent states are the solutions of corresponding Schrodinger equations described the evolution states with minimum of uncertainty (in Heisenberg sentence it is quantum states with maximum classical properties), the Hadamard transform creates the superpositon on classical states, and quantum operators as CNOT create robustness entangled states, interference is created by quantum fast Fourier transform. Structures of these operators are described.

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**148**)Principles and methodologies of quantum algorithmic gates design are considered. The possibili-ties of quantum algorithmic gates simulation on classical computers are discussed. Applications of quantum gate of nanotechnology in intelligent control are introduced.

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**154**)The universality of the quantum Fourier transform in forming the basis of quantum computing algorithms is considered. The unique universal fundamental properties of quantum computing concerning quantum superposition, entanglement and interference are all explicitly represented in terms of quantum multiparticle interferometry.

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**154**)