In the present work, a previously reported idea has been further developed. The idea is based on the earlier proposed visualization of Shor’s states. Therefore, the paper deals with some ideas of quantum physics, which constitute the basis of a set of the quantum objects, employed as q–bits, their possible structure and composition being disclosed. Quantum limit is implemented in cases where the characteristic of the quantum length defined by the de Broglie wavelength is equal to or lower than the physical size of the object. It is this condition should somehow be reflected in the composition and structure of the kantovyh Islands, which should serve as qubits. In other words, in the technological sense of dimensional quantum effects in this particular case, it is necessary to understand both the need for such facilities in the process of materializing States Shore, which would match the size (dimensions) of individual quantum islet and a critical length, describing it (the island) structure and (or) property. Also, necessary operations, performance of which at the technological level will allow for electronic unit to organize quantum computation procedure, are analyzed. It is shown that if operations with matrixes are used, the process of quantum computation can take reasonable amount of time.
In the present work, a previously reported idea has been further developed. The idea is based on the earlier proposed visualization of Shor’s states. Therefore, the paper deals with some ideas of quantum physics, which constitute the basis of a set of the quantum objects, employed as q–bits, their possible structure and composition being disclosed. Quantum limit is implemented in cases where the characteristic of the quantum length defined by the de Broglie wavelength is equal to or lower than the physical size of the object. It is this condition should somehow be reflected in the composition and structure of the kantovyh Islands, which should serve as qubits. In other words, in the technological sense of dimensional quantum effects in this particular case, it is necessary to understand both the need for such facilities in the process of materializing States Shore, which would match the size (dimensions) of individual quantum islet and a critical length, describing it (the island) structure and (or) property. Also, necessary operations, performance of which at the technological level will allow for electronic unit to organize quantum computation procedure, are analyzed. It is shown that if operations with matrixes are used, the process of quantum computation can take reasonable amount of time.
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.
Context. Nature is the relation among processes and phenomena. Nothing exists in the universe without relations. Computer is transactions of relations between data with the help of control and execution mechanisms. Quantum relations are a superposition of particles and their states. Superposition and entanglement are equivalent concepts. Entanglement is a non-local superposition of deterministic states. A quantum computer is unconditional transactions of relations between qubit data. Quantum computer is an analog device for parallel solution of combinatorial problems. Practically oriented definitions of the quantum computer concepts are the path to development of scalable quantum parallel algorithms for combinatorial problems solving. Any algorithm can be reduced to a sequence of operations without conditions, because any truth table is a collection of a complete system of conditions-states. Any sequence of actions can always be reduced to one parallel operation. Conditions and sequences arise only when the developer wants to use previously created primitive constructs to build an always non-optimal computing unit. The paradigm of quantum computer creation is determined through the use of photonic transactions on the electrons of an atom may exclude the use of quantum logic. The evolutionary path of a quantum computer from the classical one: “memory-address-transaction” (MAT) → “electron-addresstransaction” → “electron-address-quantaction” (EAQ) → state-superposition-logic. The meeting point of classical and quantum computers is photon transactions on the structure of electrons. Everything that is calculated on a quantum computer can be calculated in parallel on a classical one on account of memory redundancy. The given example is a memory-driven algorithm for modeling digital products based on qubit-vector forms of functionality description for significant performance boost of computing processes by parallel execution of logical operations. Objective. Simulation of the correct SoC-component behavior based on vector representation of the logic. Formation of the triggering development of a computing based on the superposition of the classical, quantum and analog computing process, which in its development should be based on technological qubit, tabular and vector data structures for the parallel solution of combinatorial problems. Method. MAT-computing implements any algorithms on account of transactions (read-write) in memory. Qubit-vector models for describing functionalities, which differ from known truth tables in compactness of description and manufacturability for the implementation of parallel algorithms of the synthesis and analysis of digital devices and SoC-components. Results. 1) The metric of the technological data structures, focused on parallel troubleshooting in digital systems based on the usage of two logical vector operations, was proposed for the first time. 2) The metric of relations between the individual components of QC, allowing organizing a quantum deterministic computer, has been further developed. 3) Quantum architectural solutions, that allow solving coverage problems in a quasi-parallel mode, were proposed for the first time. 4) Architectural solutions based on an analog-to-digital computing, which can be used to solve the problems of the digital systems parallel analysis, have been further developed. 5) Vector-qubit structures of the logic data, that allow a quasi-parallel simulation of digital circuits, were proposed. Conclusions. Qubit models, quantum methods and combinatorial algorithms for technical diagnostics of digital devices have been implemented, which can significantly (up to 25%) reduce the time of test synthesis, deductive modeling of faulty and correct behavior, search for defective states by introducing an innovative idea of using qubit-vector data structures for describing logical components. Comparative assessments of qubit models and methods usage show an increase in the efficiency of algorithms for modeling digital devices compared to tabular ones. The superposition of a classical, quantum and analog computer is integrally represented, which allows to find the best solutions for recognition and decision making.
Context. Nature is the relation among processes and phenomena. Nothing exists in the universe without relations. Computer is transactions of relations between data with the help of control and execution mechanisms. Quantum relations are a superposition of particles and their states. Superposition and entanglement are equivalent concepts. Entanglement is a non-local superposition of deterministic states. A quantum computer is unconditional transactions of relations between qubit data. Quantum computer is an analog device for parallel solution of combinatorial problems. Practically oriented definitions of the quantum computer concepts are the path to development of scalable quantum parallel algorithms for combinatorial problems solving. Any algorithm can be reduced to a sequence of operations without conditions, because any truth table is a collection of a complete system of conditions-states. Any sequence of actions can always be reduced to one parallel operation. Conditions and sequences arise only when the developer wants to use previously created primitive constructs to build an always non-optimal computing unit. The paradigm of quantum computer creation is determined through the use of photonic transactions on the electrons of an atom may exclude the use of quantum logic. The evolutionary path of a quantum computer from the classical one: “memory-address-transaction” (MAT) → “electron-addresstransaction” → “electron-address-quantaction” (EAQ) → state-superposition-logic. The meeting point of classical and quantum computers is photon transactions on the structure of electrons. Everything that is calculated on a quantum computer can be calculated in parallel on a classical one on account of memory redundancy. The given example is a memory-driven algorithm for modeling digital products based on qubit-vector forms of functionality description for significant performance boost of computing processes by parallel execution of logical operations. Objective. Simulation of the correct SoC-component behavior based on vector representation of the logic. Formation of the triggering development of a computing based on the superposition of the classical, quantum and analog computing process, which in its development should be based on technological qubit, tabular and vector data structures for the parallel solution of combinatorial problems. Method. MAT-computing implements any algorithms on account of transactions (read-write) in memory. Qubit-vector models for describing functionalities, which differ from known truth tables in compactness of description and manufacturability for the implementation of parallel algorithms of the synthesis and analysis of digital devices and SoC-components. Results. 1) The metric of the technological data structures, focused on parallel troubleshooting in digital systems based on the usage of two logical vector operations, was proposed for the first time. 2) The metric of relations between the individual components of QC, allowing organizing a quantum deterministic computer, has been further developed. 3) Quantum architectural solutions, that allow solving coverage problems in a quasi-parallel mode, were proposed for the first time. 4) Architectural solutions based on an analog-to-digital computing, which can be used to solve the problems of the digital systems parallel analysis, have been further developed. 5) Vector-qubit structures of the logic data, that allow a quasi-parallel simulation of digital circuits, were proposed. Conclusions. Qubit models, quantum methods and combinatorial algorithms for technical diagnostics of digital devices have been implemented, which can significantly (up to 25%) reduce the time of test synthesis, deductive modeling of faulty and correct behavior, search for defective states by introducing an innovative idea of using qubit-vector data structures for describing logical components. Comparative assessments of qubit models and methods usage show an increase in the efficiency of algorithms for modeling digital devices compared to tabular ones. The superposition of a classical, quantum and analog computer is integrally represented, which allows to find the best solutions for recognition and decision making.
A computer is a physical device that helps us process information by executing algorithms. An algorithm is a well-defined procedure, with finite description, for realizing an information-processing task. An information-processing task can always be translated into a physical task. When designing complex algorithms and protocols for various information-processing tasks, it is very helpful, perhaps essential, to work with some idealized computing model. However, when studying the true limitations of a computing device, especially for some practical reason, it is important not to forget the relationship between computing and physics. Real computing devices are embodied in a larger and often richer physical reality than is represented by the idealized computing model. Quantum information processing is the result of using the physical reality that quantum theory tells us about for the purposes of performing tasks that were previously thought impossible or infeasible. Devices that perform quantum information processing are known as quantum computers. In this book we examine how quantum computers can be used to solve certain problems more efficiently than can be done with classical computers, and also how this can be done reliably even when there is a possibility for errors to occur. In this first chapter we present some fundamental notions of computation theory and quantum physics that will form the basis for much of what follows. After this brief introduction, we will review the necessary tools from linear algebra in Chapter 2, and detail the framework of quantum mechanics, as relevant to our model of quantum computation, in Chapter 3. In the remainder of the book we examine quantum teleportation, quantum algorithms and quantum error correction in detail. We are often interested in the amount of resources used by a computer to solve a problem, and we refer to this as the complexity of the computation. An important resource for a computer is time. Another resource is space, which refers to the amount of memory used by the computer in performing the computation. We measure the amount of a resource used in a computation for solving a given problem as a function of the length of the input of an instance of that problem.
It was Richard Feynman who first proposed, in 1982, the far-reaching concept of \na ”quantum computer”—a device more powerful than classical computers. The idea \nof a quantum computer is to employ the fascinating and often counterintuitive \nlaws of quantum mechanics to process information. It is far from obvious that \nthe proposed concept of a quantum computer is more powerful than its classical \ncounterpart, it was only in 1994 when Peter Shor theoretically demonstrated the \nexistence of a quantum algorithm for factorizing integers into prime factors \nthat runs in polynomial time unlike its classical counterpart which works in \nsub-exponential time. The factorization of integers into prime factors is the \nbasis of asymmetric cryptography. These early theoretical results lunched an \nimmense interest of the scientific community. Already during ’90s, the first \nproposals for the physical implementation of quantum computation emerged. Ever \nsince, many experimental groups around the world pursued different physical \nimplementations of quantum bits (qubits). The first decade of the new century \nsaw a steady improvement in the control and decoherence time (the time over \nwhich the information carried by the qubit is lost) for various qubits by many \norders of magnitude. The natural next step in this context is to answer the \nquestion of how to scale the system up to include many qubits and thus build a \nquantum computer? One of the main parts of this thesis addresses exactly this \nquestion, namely the question of architecture and scalability of future quantum \ncomputer. \n \nAmong various different physical realizations of qubits, the idea of using \nelectron spins trapped in electrostatic semiconductor quantum dots as the \nbuilding blocks of a quantum computer (the so-called spin qubits), put forward \nby Daniel Loss and David DiVincenzo in 1997, triggered tremendous interest in \nscientific community. Nevertheless, the implementation of the original \nLoss-DiVincenzo proposal posed a considerable technical challenge. It used \nquantum tunneling between qubits to enable their communication with each other, \nand thus required that the qubits to be placed very close to each other. This \nrequirement not only leaves little \nspace for the placement of the vast amount of gates and wirings needed to define \nthe electrostatic quantum dots, but also makes it challenging to control the \nlocal magnetic field needed for single-qubit operations. For these reasons, no \nsystem with more than a couple of spin qubits has been \nsuccessfully implemented thus far. In the first part of this thesis, we leap \nover this long-standing problem with an entirely different strategy of using \nmetallic floating gates or ferromagnets to couple together qubits that are \nseparated over a long distance. Our scheme works for any type of \nspin qubits, including the qubits based on nitrogen-vacancy center (NV-center) \nin diamond and technologically very important silicon qubits. \n \nThe main topic of this thesis is related to quantum computer. Still, quite \nunexpectedly, some of the ideas we employed in order to tackle the problem of \nquantum computer scalability can be utilized in a completely different field of \nresearch, namely, in the field of magnetic field sensing. Qubit are not only a \nnecessary ingredient of quantum computer but they also provide a way to measure \nvery accurately magnetic fields. The magnetometer build upon the qubit based on \nNV-center, so-called NV-magnetometer, emerged in recent years as most sensitive \nmagnetic moment sensor. These magnetometers are able to detect about hundred \nnuclear spins within a minute of acquisition time. In the second part of this \nthesis, we propose an entirely novel experimental realization of \nNV-magnetometers which increases present NV-center sensitivities by four orders \nof magnitude at room temperature. This unprecedented amplification of \nsensitivity will render magnetometers capable of detecting individual nuclear \nspins. This amplification is achieved by introducing a ferromagnetic particle \nbetween the nuclear spin that needs to be detected and the NV-magnetometer. Our \nsetup, in contrast to existing schemes, is particularly advantageous because, \ndue to the large amplification of sensitivity, the nuclear spin need not lie \nwithin a few nanometers of the surface but rather can be detectable at a \ndistance of 30 nm. With these novelties, our scheme provides chemically \nsensitive spin detection under ambient conditions allowing nanoscale resolution \nof nuclear magnetic moments in biological systems—the holy grail of nuclear \nmagneticresonance. \n \nIn the last part of the thesis we focus our attention to a new direction in \nquantum computer implementation that deals with topological quantum computer \nintroduced by Alexei Kitaev in 1997; in this approach the idea is to use \nquasiparticles with ”fractional” statistics and to perform the single- and \ntwo-qubit gates by merely exchanging these quasiparticles. Additionally, \ninformation in this system is stored non-locally thus it mitigates the problem \nof decoherence caused by local noise from the environment. Majorana fermions are \none of the most well known examples of such excitations. We analyze transport \nsignatures of different topological states in one-dimensional systems, like \nMajorana fermions and fractionally charged states. We envision an Aharonov-Bohm \nsetup wherein conductance measurement provides a clear signature of presence of \nfractionally charged fermionic states, since oscillations with double period \nemerge in this case. Additionally, we propose a very simple setup that enables \nexistence of degenerate mid-gap states, so-called Tamm-Shockley states that are \ncharacterized by fractional charge and discuss possible ways of detecting these \nstates experimentally. \n
In the twentieth century, quantum physics is one of the most successful approaches in scientific progress. To theorize the concept of quantum computing Max Planck's idea of the existence of energy in individual units like matter was used. Since then, the idea of manufacturing quantum computers for everyday use is becoming more plausible with technological advances in quantum theory. A classical computer carries out logical operations using a bit which is either 1 or 0. In contrast to a classical computer, a quantum computer works with a quantum bit or qubit, which is not limited to two states only. Qubits can exist in a superposition of the two states creating parallelism. Qubit represents the state of atoms, ions, photons or electrons. These qubits which work together with a control device act as a computer memory.Quantum computers have the potential to become million times more potent than present-day supercomputers due to the presence of these multiple states simultaneously. Concepts and ideas of quantum computing have been demonstrated by different methods like Ion Trap, Quantum Dot methods etc. However, the actual realization of such a superior system is still in the future. A strategy must be formulated to maintain decoherence and other potential sources of error at a permissible level.Astonishingly, quantum computing took a long time to take off, even though the physicists have known about the world of subatomic particles. Even so, it took computer scientists another half-century to consider harnessing quantum effects for computation. Also, it was later discovered that quantum computers could solve quantum mechanical many-body problems that are impractical to solve on a classical computer. The foundations of the subject of quantum computation may have become well-published, but the knowledge is still growing. Hence here is a research paper based on the study of quantum computation.