Von Neumann Quantum Logic vs. Classical von Neumann Architecture?

The name of John von Neumann is common both in quantum mechanics and computer science. Are they really two absolutely unconnected areas? Many works devoted to quantum computations and communications are serious argument to suggest about existence of such a relation, but it is impossible to touch the new and active theme in a short review. In the paper are described the structures and models of linear algebra and just due to their generality it is possible to use universal description of very different areas as quantum mechanics and theory of Bayesian image analysis, associative memory, neural networks, fuzzy logic. J. von Neumann is considered as one of " fathers " of modern computers due to his theoretical works and elaboration of computer EDVAC at 1945–50, but already 20 year before it, at 1926–31 he participated in drawing yet another kind of logic — logic of quantum mechanics and only now the different areas of research of one scientist seem going to meet and born new family of ultrascale cybernetic devices — quantum computers. Currently the quantum information science exists mainly as theoretical area of research and size of quantum registers does not exceed of 3–5 quantum bits (qubits), but in the paper is considered question: does the quantum logic has some useful application as an abstract mathematical model in computer science? Such applications of physical models nowadays are not unusual, for example Boltzmann machines and other methods came to area of artificial neural networks from statistical physics [1, 2]. It is also useful to draw some analogy with fuzzy sets and logic [3]. Here is used discrete representation of 2D sets on some lattice due to understanding analogy with bit-map pictures. Let us introduce few data types in some " Pascal-like " notation to come from fuzzy sets to quantum registers. Here n and N = 2 n are integer numbers.