Quantum Models for Description of Digital Systems - Hahanov, V. I.; Hahanova, I. V.; Litvinova, E. I.; Priymak, A.; Fomina, E.; Maksimov, M.; Tiecoura Yves; Malek Jehad Mohammad Jararweh (EWDTS, 2013)
Quantum models for description of digital systems and results of studies concerning the models and methods of quantum diagnosis of digital systems, qubit fault simulation and analysis of fault-free behavior are presented. Quantum calculators are effectively used for faulttolerant design and solving optimization problems by way of the brute-force method through the use of set theory. A set of elements in the traditional computer is orderly, because each bit, byte or other component has its own address. Therefore, the settheoretical operations are reduced to exhaustive search of addresses of primitive elements. Address order of data structures useful for applications where model components can be strictly ranked, which makes it possible to carry out their analysis in a single pass (a single iteration). If there is not order in the structure, for example, the set of all subsets, the classical model of memory and computational processes disimprove the analysis time of primitive association equal by the rank, or processing of associative groups is ineffective. What can be offered for unordered data instead of the strict order? Processor, where the unit cell is the image or pattern of the universe of n primitives, which generates nQ 2 = all possible states of a cell as a power set or the set of all subsets. Direct solution about creating such cell is based on unitary positional coding states of primitives that form the set of all subsets and in the limit the universe of primitives by superposition of last ones. History of the issue of the necessity for developing quantum computing on the background of the technological revolution in nano-electronics fit in a few of clear theses: 1) Quantum Computer was created the experts in the field of quantum mechanics and electronics, who introduced the idea of creating a non-numeric analogbased computer. 2) The introduced notion of a qubit corresponds to the power set of primitives, which is the ideal nonnumeric form of object component description for analysis, synthesis and optimization of discrete objects. 3) The forms of qubit representation are the following: 1. The universe of primitive symbols, which generate the set of all subsets (power set). 2. Binary vectors, where the power set is a combination of unit values of primitives. 3. Hasse diagram, which forms the power set of all possible solutions on the graph. 4. Full transition graph, which determines the set of all subsets of transitions in the form of arcs. 5. The geometric representation in a plane for a qubit in the form of points and segments corresponding to the Boolean (power set). 4) In practice, more than 90% of all IT-industry problems associated with information retrieval in cyberspace, pattern recognition and decision-making are related to the field of discrete mathematics, where it is difficult to find a place of numerical arithmetic. 5) It is necessary to create associative logic brainlike parallel (quantum) processors, which effectively use Boolean (qubit) primitives or elements (sets) to solve problems of discrete mathematics. 6) Set-theoretic operations have to be replaced the isomorphic logical instructions (and, or, not, xor) for the subsequent creating a new system of parallel qubit programming to solve logic and optimization problems, based on qubit data structures. 7) Another solution for organization computing is associated with topological representation of the qubit, where the elements are the geometric shapes. 8) Nonnumeric problems, focused to the use of quantum processor are the following: minimization of forms of Boolean functions, when describing complex systems; searching paths in the graph; testing and diagnosis of digital systems; combinatorial studies of processes and phenomena; intelligent data searching, pattern recognition and decision making; discretization of fuzzy models and methods, when creating the intelligence; digital data processing and the developing efficient codec for DSP-devices.
Keywords: Quantum Models; Description of Digital Systems