A methodical analysis of the basic problem related to quantum calculations of parameters of physical systems was made. Emphasis is placed on the physical principles of the operation of a quantum computer, with an emphasis on the fact that simultaneous access to all quantum states is important in quantum computing, which allows the simultaneous change of the quantum state from all superpositions in the qubit system. Emphasis is placed on the fact that in quantum algorithms the Fourier transform and the Hadamard transform are the basic operations - as a simple discrete Fourier transform. The reader's attention is drawn to the fact that quantum computing is primarily implemented in quantum objects with the properties of elementary NOT gates and controlled CNOT, which can be implemented on a Mach-Zehnder interferometer using the phenomena of photon interference and rotation of its polarization vector. Despite the progress of conventional computers, the need for the development of quantum computing is due to the technological limitation due to the dimensional quantization of the electronic spectrum and the exponential increase in the time of calculations by classical algorithms when the volume of data increases. However, the widespread use of quantum computers is limited by a number of problems. This is, first of all, insufficient accuracy and high sensitivity to external influences that can destroy the quantum state. Therefore, to increase the accuracy of calculations on a quantum computer, the calculation algorithm must be repeated a certain number of times, and to avoid the destruction of the quantum states of the qubit, low temperatures are used.
A methodical analysis of the basic problem related to quantum calculations of parameters of physical systems was made. Emphasis is placed on the physical principles of the operation of a quantum computer, with an emphasis on the fact that simultaneous access to all quantum states is important in quantum computing, which allows the simultaneous change of the quantum state from all superpositions in the qubit system. Emphasis is placed on the fact that in quantum algorithms the Fourier transform and the Hadamard transform are the basic operations - as a simple discrete Fourier transform. The reader's attention is drawn to the fact that quantum computing is primarily implemented in quantum objects with the properties of elementary NOT gates and controlled CNOT, which can be implemented on a Mach-Zehnder interferometer using the phenomena of photon interference and rotation of its polarization vector. Despite the progress of conventional computers, the need for the development of quantum computing is due to the technological limitation due to the dimensional quantization of the electronic spectrum and the exponential increase in the time of calculations by classical algorithms when the volume of data increases. However, the widespread use of quantum computers is limited by a number of problems. This is, first of all, insufficient accuracy and high sensitivity to external influences that can destroy the quantum state. Therefore, to increase the accuracy of calculations on a quantum computer, the calculation algorithm must be repeated a certain number of times, and to avoid the destruction of the quantum states of the qubit, low temperatures are used.
Abstract: Quantum computing is a modern calculation method that is based on the science of quantum mechanics. These phenomena include the bizarre behavior of particles at the atomic and subatomic levels, and the way that these particles can be in multiple states simultaneously. The field of computer science is a great mix of physics, math, and information theory. This technology provides high computing power, low power consumption, and exponential speed by controlling the behavior of small physical objects, such as atoms. Atoms, electrons, photons, etc. are all elements of the physical world. We would like to introduce the basics of quantum computing, and some of the ideas behind it. This article begins with the origins of the classical computer and discusses all the improvements and transformations that have been made due to its limitations thus far, then moves on to the basic operations of quantum computing and results in quantum properties such as superposition, entanglement, and interference.
Summary form only given, as follows. Gives a system theoretic approach to the concept of quantum computing. A quantum computer is envisaged to be a system of quantum circuits, acting on a state space, which is a finite-say 2/sup n/-dimensional-complex Hilbert space. The circuitry is a sequence of unitary transforms U/sub t/ /spl epsiv/ SU(2/sup n/) followed by a measurement. These transforms, so-called quantum gates, are controlled by a classical computer, usually especially electromagnetic fields. The state space of a quantum computer has the structure of a Hermitian vector space. Thus it allows "simultaneous" superposition of orthogonal basis states (corresponding to classical states) with the possibility of constructive and destructive interference between different paths of computation. This principle allows the usage of so-called entangled states by preparing the superposition of special "bent" configurations of basis vectors in the product Hilbert space, e.g., as they are known from error control and cryptography. This latter "entanglement" not only promises to make a quantum computer much more powerful than a probabilistic one, but it also allows a method of parallelism. The reason for this lies not only in the fact that the 2/sup n/ dimensional Hilbert space is the n-fold tensor product of 2-dimensional spaces as it is given by spin-1/2-particles, like photons, representing a quantum bit. First of all, we shall address the fact that the power of quantum computing lies in the properties of entangled states as opposed to those of separable states which essentially would resemble classical circuits without giving the feature of exponential speed-up. We shall briefly describe possible physical realisations of quantum (optic, electronic, magnetic,...) devices allowing the engineering of Hamiltonians needed for quantum systems. Basic quantum gates, especially the quantum Horner-Toffoli gate will be discussed to display the principles and methodology for designing quantum circuits. An outlook towards the possible availability of nano- and mesoscopic technologies supporting this new architecture in future generations concludes based on a speculative worst/best case forecast of possible applications, e.g., in public key and conventional cryptography.
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.
Quantum computing represents a transformative paradigm that exploits the principles of quantum mechanics—superposition, entanglement, and quantum interference—to perform computations beyond the capabilities of classical computers. This review presents a comprehensive overview of the fundamental concepts underlying quantum computation, including qubits, quantum gates, quantum algorithms and measurement theory. It further examines major physical implementations of quantum computers, such as superconducting circuits, trapped ions, photonic systems, spin-based qubits, and topological approaches, highlighting their operational principles, advantages, and technological limitations. Key challenges hindering large-scale quantum computation—decoherence, error rates, qubit scalability, and fault tolerance—are critically discussed. Additionally, recent progress in quantum error correction, hybrid quantum–classical algorithms, and hardware optimization is summarized. The review concludes by outlining future research directions and potential applications of quantum computing in cryptography, materials science, optimization, and drug discovery. By integrating theoretical foundations with experimental advancements, this article aims to provide a clear and accessible reference for students, researchers, and scientists entering the rapidly evolving field of quantum computing.
Quantum computing represents a monumental leap in computational technology, leveraging the principles of quantum mechanics to solve complex problems at unprecedented speeds. Unlike classical computers, which rely on bits as the smallest unit of information, quantum computers utilize qubits that can exist in multiple states simultaneously, enabling them to perform many calculations at once. This paper delves into the foundational concepts of quantum computing, including superposition, entanglement, and quantum gates, and explores its potential applications across various domains, such as cryptography, drug discovery, optimization problems, and artificial intelligence. We will discuss current advancements in quantum technology, high-lighting key breakthroughs and the progress made by leading research institutions and companies. Furthermore, this paper addresses the significant challenges that quantum computing faces, including error rates, qubit coherence, and scalability, which hinder its widespread adoption. By examining these facets, we aim to provide a comprehensive overview of how quantum computing could transform various fields and the hurdles that must be overcome to realize its full potential, ultimately suggesting future directions for research and development in this revolutionary area of technology.
This presentation provides a comprehensive overview of the foundational principles of quantum computation. It begins by contrasting classical and quantum information, highlighting how quantum bits (qubits) leverage superposition, entanglement, and interference to process information in ways that surpass classical limits. The document explains the four postulates of quantum mechanics: state space (qubits as unit vectors in a Hilbert space), time evolution (via unitary operators), measurement (probabilistic collapse of the state), and composite systems (tensor products of subsystems). Key concepts such as the Bloch sphere representation, quantum gates (e.g., Hadamard, CNOT, Pauli gates), and quantum circuits are discussed, illustrating how quantum operations manipulate qubit states. The presentation also covers quantum evolution, the gate model for computation, and the universality of certain gate sets, emphasizing the potential for quantum parallelism and the transformative impact of quantum computing on fields like cryptography and optimization.