Modern physical picture of the world is a quantum field and requires specific conceptual and mathematical apparatus. Practically, each concept is supplied by means of some mathematical structures from branches of mathematical and functional analysis, for the qualitative understanding which required independent decision by the student to practice specific physical problems. Design of information models of the physical processes allows us to comprehend the task as the object or phenomenon of the physical reality, to analyze it using various mathematical methods, to develop algorithm and the program of the interchange on the computer. The file contains data on the calculation of the wave functions of the first three stationary states of an electron in a potential well of a special type, which were presented in work Turinov A., Galdina A. Application Of Computer Modeling To Solving Quantum-Mechanical Problems // Physical and Mathematical Education : scientific journal. – 2017. – Issue 3(13). – Р. 170-177 (available at https://fmo-journal.fizmatsspu.sumy.ua/journals/2017-v3-13/2017_3-13-TurinovGaldina_Scientific_journal_F.pdf). Calculations were made in Wolfram Mathematica. The energies of these states were also calculated and the corresponding graphs were plotted.
Modern physical picture of the world is a quantum field and requires specific conceptual and mathematical apparatus. Practically, each concept is supplied by means of some mathematical structures from branches of mathematical and functional analysis, for the qualitative understanding which required independent decision by the student to practice specific physical problems. Design of information models of the physical processes allows us to comprehend the task as the object or phenomenon of the physical reality, to analyze it using various mathematical methods, to develop algorithm and the program of the interchange on the computer. The file contains data on the calculation of the wave functions of the first three stationary states of an electron in a potential well of a special type, which were presented in work Turinov A., Galdina A. Application Of Computer Modeling To Solving Quantum-Mechanical Problems // Physical and Mathematical Education : scientific journal. – 2017. – Issue 3(13). – Р. 170-177 (available at https://fmo-journal.fizmatsspu.sumy.ua/journals/2017-v3-13/2017_3-13-TurinovGaldina_Scientific_journal_F.pdf). Calculations were made in Wolfram Mathematica. The energies of these states were also calculated and the corresponding graphs were plotted.
The article deals with new approaches in studying the features of the structure and principles of functioning of quantum computers, as one of the components of the elemental base of modern computer electronics, due to more efficient layout and supply of the corresponding lecture material using the multimedia presentation system. It is shown that at the present stage of the creation of quantum computers goes in two directions: specialized quantum computers that are aimed at solving one particular specific task, such as optimization tasks (quantum computers D-Wave); and universal quantum computers that are capable of implementing arbitrary quantum algorithms (Shore, Simon, Grover) - in implementing from IBM, Google, etc. The work of quantum registers is analyzed. When processing this material, students show that the ability of devices that are based on the classical principles of computing machines, in recent years reached a level in which most tasks can be solved relatively quickly and quite accurately. However, in various areas of knowledge, there are problems to decide which, including using the best supercomputers of the world, is not possible. After all, modern transistors have already reached a few nanometers, and in the future, electronic semiconductor components cannot be reduced infinitely, because their elements will consist of one atom. The development of classical computers in the form of cloud computing capacities is also limited in the area and consumed energy. In addition, not each algorithm is subject to parallelization. Effective processing of large volumes of data requires high-performance computations in the field of artificial intelligence, science-intensive industrial areas, modeling of chemical and physical phenomena and processes, that is, where it ceases to have the capabilities of modern supercomputers. Solving this problem is possible to apply the latest technologies of quantum computers. It has been shown that the quantum computer is a computing device that uses the phenomenon of quantum superposition (parallelism) and quantum confusion to transmit data and data processing, that is, the basis of its central processor is laid logic of quantum mechanics using special quantum algorithms. Such a computer is fundamentally different from a traditional computer that perceives any information in the form of a binary code, which may be in one of two possible states: 0 or 1. Any classic processor represents these two states of low or high voltage levels inside the semiconductor transistor. Its task to select zero or unit. Quantum processors are made according to the same principle, but a radical cancellation that instead of a transistor, they use kubit (Qubit) – quantum bits.
The article is devoted to the actual problem of teaching methods of the subjects of the educational process of modern information and computer science. The contribution of Ukrainian scientists to the development of electronic computing machines, their programming and teaching methods, prospects for further research are briefly considered. In the natural sciences, elementary units are widely used for various measurements. In particular, Planck’s constant is the smallest portion, quantum of energy, quantum of action, which is used in quantum mechanics. It is also known from the course of physics that the smallest portion of energy in classical mechanics is the energy per one degree of freedom. Logically created mathematical models and theories describing the relevant properties of matter using the specified units. Similarly, emphasis is placed on clarifying the difference between a classical computer and quantum units of information. The concepts of bit of information, qubit and trit are revealed, and depending on the defined units of information, types of computers are distinguished: classical and quantum. The concepts of qubit and trit are considered mainly as a mathematical entity, and attention is not focused on the content of the physics of quantum objects, a comparison of the indicated units of quantum information with a traditional bit of information in the quantum world is given. A historical-genetic analysis of the registers of elementary logic systems, a theoretical study of the principles of superposition and interaction between quantum states, and experimental methods of implementing qubits and their connections have been carried out. An important field for the use of quantum computers is cryptology, for solving the problems of which Grover’s method has already been created. With Grover’s quantum algorithm, it is possible to quickly search for the necessary element in an unsorted database with 2nN (n is the length of the search space of the quantum register - the number of qubits in it; N is the size of the search space). However, although the quantum simulator gives a high probability of the correct result, experimental studies also show large discrepancies. Therefore, there is a problem for further research. Quantum computers can influence each other through the phenomenon of entanglement.
The process of mathematical modeling of the electron motion in a potential well of finite depth using a virtual laboratory is considered. Despite the fact that quantum physics has existed for more than a century, its laws were studied only with the help of mathematical formulas, and the probability density of the wave function describing the microparticle was determined. With the help of mathematical formulas, the values of discrete energy distributions, as well as the wave function of the microparticle, were determined. In this scientific article, a wave function of electron motion in a finite potential well and its discreteness relative to the values of energy quantum numbers are obtained using a special program. If the principal quantum number is equal to one, the wave function has only one curve, if the principal quantum number is equal to two, it has a curve with two peaks, if the principal quantum number is equal to three, it has a curve with three peaks, and if the principal quantum number is equal to four, it has a curve with four peaks. Between each quantum number, there are no values of the wave function density, which corresponds to forbidden zones, while in the areas where there is a w
This work presents a brief review on the modern approaches to data modeling by the methods developed in the quantum physics during the last one hundred years. Quantum computers and computations have already been widely investigated theoretically and attempted in some practical implementations, but methods of quantum data modeling are not yet sufficiently established. A vast range of concepts and methods of quantum mechanics have been tried in many fields of information and behavior sciences, including communications and artificial intelligence, cognition and decision making, sociology and psychology, biology and economics, financial and political studies. The application of quantum methods in areas other than physics is called the quantum-like paradigm, meaning that such approaches may not be related to the physical processes but rather correspond to data modeling by the methods designed for operating in conditions of uncertainty. This review aims to attract attention to the possibilities of these methods of data modeling that can enrich theoretical consideration and be useful for practical purposes in various sciences and applications.
This is explored in this work by constructing and analyzing theoretical models explaining how this works. It focuses on such mathematical objects as Hilbert spaces, operators and wave functions and looks at the way these mathematical components of the edifice manifest quantum states and observables. The purpose of this work is the enrichment of the knowledge about quantum processes including superposition and entanglement, and the creation of new systems of theories and elaboration of the old ones. It is a methodology that involves application of a set of strict proofs, operator theory and functional analysis with regard to the real world mathematical concepts that are not easily understood. Its results mean the relevance of advanced mathematical tools in the understanding of the workings of quantum systems and serve to open the prospect of more plausible models that could lead to the impact of quantum computing and information theory. This research is relevant to the overall education that is needed to enable the creation of theoretical physics and applied quantum technologies.
Recently, there has been a rapid increase in interest in quantum computers. Their work isbased on the use of quantum-mechanical phenomena such as superposition and entanglement forcomputing input data into output data that can actually provide effective performance 3 to 4 orders ofmagnitude higher than any modern computing devices, which will solve the above and others tasks ina natural and accelerated time scale. This article is devoted to solving the problem of research anddevelopment of corrective codes for correcting several types of quantum errors that appear duringcomputational processes in quantum algorithms and models of quantum computing devices. The aimof the work is to study existing methods for correcting various types and types of quantum errors andto create a 3-qubit corrective code for quantum error correction. The work touches upon the tasks ofresearch and development of the functioning methods of quantum circuits and models of quantumcomputing devices. The relevance of these studies lies in the mathematical and software modelingand implementation of corrective codes for correcting several types of quantum errors as part of thedevelopment and implementation of quantum algorithms for solving classes of classical problems.The scientific novelty of this area is expressed in the exclusion of one of the shortcomings of thequantum computing process. The scientific novelty of this area is primarily expressed in the constantupdating and addition of the field of quantum research in a number of areas, and computer simulation of quantum physical phenomena and features is poorly illuminated in the world. The aim of the work is computer simulation of a quantum computing process using the method of correctingphase types of errors, which allows one to evaluate the own phase of a unitary gate that hasgained access to the quantum state in proportion to its own vector.