Quantum Informatics: Overview of the Main Achievements

Abstract

The urgency of conducting research in the field of quantum informatics is grounded. Promising areas of research are highlighted. For foreign and Russian publications and materials, a review of the main scientific results that characterize the current state of research in quantum computer science is made. It is noted that knowledge and funds are invested most intensively in the development of the architecture of a quantum computer and its elements. Despite the fact that today there is no information on the creation of a physical implementation of a quantum computer comparable in functionality to a classical digital computer, the development of quantum algorithms is one of the popular areas of research. An advantage of quantum algorithms is the fact that they reduce the time required to solve the problem due to the parallelization of operations by generating entangled quantum states and their subsequent use. This advantage (quantum acceleration) is most important when solving the problem of modeling the dynamics of complex systems and enumerated mathematical problems. (The general case of enumeration is the Grover scheme and its variants; the tasks of searching for hidden periods: Shor's scheme of using the fast quantum Fourier transform and its analogues.) The demand for cybersecurity developments (search for vulnerabilities in smart spaces, secure storage and use of big data, quantum cryptography) is noted. More than a dozen articles are devoted to quantum algorithms of key search, key distribution on optical fibers of various lengths, and the analysis of quantum resources necessary for conducting a cyber attack. In the field of artificial quantum intelligence, attention is paid, first of all, to the “search” for a model of a quantum neural network that is optimal from the point of view of using all the advantages presented by quantum computing and neural networks, as well as machine learning algorithms. Examples of the use of quantum computing in cognitive and social sciences for studying the decision-making mechanism with incomplete data are given. It is concluded that quantum informatics is promising for the simulation of complex natural and artificial phenomena and processes.

Smashed and Twisted Wreath Products of Metagroups

“…Using the embedding C V → F and Equation (35), we infer that (d 1 , f 1 Lemma 5, and Equation (30). It can be verified similarly that F * is the almost normal subloop in C * .…”

“…The results of this article can be used for further studies of metagroups, quasi-groups, loops, and noncommutative manifolds related with them. Besides applications of metagroups, loops, and quasi-groups outlined in the introduction, it is interesting to mention possible applications in mathematical coding theory and classification of information flows and their technological implementations [28][29][30] because, frequently, codes are based on binary systems. Moreover, twisted products are used for creating complicated codes [22].…”

“…Then, we choose a central metagroup B generated by an element b 0 and a commutative group C 1 such that b 0 / ∈ C 1 , C m (D) → C 1 and C(A) → C 1 and the quotient group B/C m (B) is of finite order l > 1. Then, let φ : A → A(B) satisfy the condition of Equation (30) and be such that…”

Structure of Normed Simple Annihilator Algebras

“…Other possible applications are in mathematical coding theory and its technical implementations [38][39][40], because frequently codes are based on binary systems and algebras over non-Archimedean fields. Idempotents and decompositions of operator algebras can be used for an analysis and a classification of flows of information [22,41] and a solution of related PDEs [27,42].…”

Research and Study of the Hybrid Algorithms Based on the Collective Behavior of Fish Schools and Classical Optimization Methods

“…Such decisions are based on recognized underlying relationships in datasets. Neural networks take in a vector encoding the input object; the output signal of a neural network encodes the decision made by the system [38]. A perceptron is a mathematical model, proposed by Frank Rosenblatt in 1957; it can be treated as a simple neural network used to classify the data into two classes.…”