The article provides an approach of modeling quantum states which determine the properties of an abstract system, means the design and simulation environment Matlab, as well as means of instrumental package Simulink. Describes the representation of a quantum system in two ways: in the form of the state vector and in the form of density matrices. Considered unary, binary and ternary logical operations on qubits, called quantum converters. The process of assignment of qubits, the method of imaging, the use of quantum transformation to qubits, and visualization of results of converters in the environment Matlab are described. Developed a model that shows the use of the converter two qubits converter controlled NOT (CNOT), followed by visualization of the results of his work in the visual simulation system Simulink. Conclusions are drawn on applicability of the Matlab/Simulink environments to problems of modeling of quantum systems.
The article provides an approach of modeling quantum states which determine the properties of an abstract system, means the design and simulation environment Matlab, as well as means of instrumental package Simulink. Describes the representation of a quantum system in two ways: in the form of the state vector and in the form of density matrices. Considered unary, binary and ternary logical operations on qubits, called quantum converters. The process of assignment of qubits, the method of imaging, the use of quantum transformation to qubits, and visualization of results of converters in the environment Matlab are described. Developed a model that shows the use of the converter two qubits converter controlled NOT (CNOT), followed by visualization of the results of his work in the visual simulation system Simulink. Conclusions are drawn on applicability of the Matlab/Simulink environments to problems of modeling of quantum systems.
Abstract The aim of the research is computer simulation of a quantum algorithm to solve the problem of transforming a classical image using quantum computing tools and methods, studying recognition algorithms and creating a recognition model using quantum methods. The method of quantum modeling makes it possible to convert a classical image into a quantum state, select boundaries and convert a grayscale image to a binary one, and shows the possibilities of the quantum information theory in interpreting classical problems. The main results of the article are the developed quantum algorithm that allows recognizing objects, as well as the quantum method aimed at representing/processing a color pixel image. The scientific novelty of the article is expressed in the construction of a quantum system, an exponential increase in the speed of solving computational NP-complete problems, which on classical machines can be solved in unacceptable time. The motivation for writing the work was a high growth interest in quantum computing and the benefits that they guarantee. The development of the theoretical foundations of creating software systems and the design of algorithms for new information technologies and specialized computing systems is a dynamic field, as evidenced by the number of existing works in this direction. The developed algorithms for various problems of complexity classes can give a significant gain in efficiency in comparison with existing classical ones and provide a solution to a number of complex mathematical (including cryptographic) problems.
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.
The paper describes the simplest technique for simulating a quantum algorithm based on the direct matrix representation of quantum operators.This approach is stable and precise, but it requires allocation of operator's matrices in the computer memory.Since the size of the operators grows exponentially, this approach is useful for simulating quantum algorithms with a relatively small number of qubits (e.g., approximately 11 qubits on a typical desktop computer).This approach enables relatively simple simulation of the operation of the solution quality control system and performance of a reliability analysis.A more efficient fast quality control simulation method is based on computing all or a part of operator matrices as needed on a current computational basis.This method makes it possible to avoid storing all or a part of the operator matrices.In this case, the number of qubits to be simulated (e.g., the number of input qubits or the number of qubits in the system state register) is affected by: (I) the exponential growth in the number of operations required to calculate the result of matrix products; and (II) the size of the state vector allocated in computer memory.It is reasonable if one embodiment of this approach involves simulating up to 19 or more qubits on typical desktop computer, and even more in a system with a vector architecture.Due to particularities of the memory addressing and access processes in a typical desktop computer (such as, for example, a Pentium PC), when a number of qubits is relatively small, the on-demand computing tends to be faster than the direct storage approach.The compute-on-demand approach benefits from applying the results of studying quantum operators and their structure that enables computing the matrix elements more efficiently.The paper considers effective simulation of Grover's quantum search algorithm using a computer with classical architecture.
Most proposals for quantum neural networks have skipped over the implementation of the Qubit, superposition, entanglement and measurement in order to be used in MATLAB environment. Quantum computing uses unitary operators acting on discrete state vectors. Matlab is a well-known (classical) matrix computing environment, which makes it well suited for simulating quantum algorithms. The Quantum Computing Function (QCF) library extends Matlab by adding functions to represent and visualize common quantum operations. On the other hand a new mathematical model of computation called Quantum Neural Networks (QNNs) is defined, building on Deutsch's model of quantum computational network. The Quantum Neural Network (QNN) model began in order to combine quantum computing with the striking properties of neural computing. In this paper the use and importance of those functions is illustrated with the help of few examples. This paper presents a brief overview of QCF that how it can be useful in Quantum Neural Network simulation.
This article explores and develops a method for the functioning of quantum algorithms and models of quantum computing devices to transform a classical image into a quantum state, highlight boundaries and convert a halftone image into a binary one. The presented quantum algorithm demonstrates the prospects for applying quantum information theory to solve classical problems. The main emphasis of the work is on computer simulation of a quantum algorithm and the study of its effectiveness when using quantum computing tools and methods. The relevance of this research stems from the constant updating and expansion of the field of quantum research, as well as from the lack of computer simulations of quantum physical phenomena. The scientific novelty of the work lies in the development of an effective pattern recognition model using the properties and methods of quantum computing, which contributes to the development of this area of scientific research.
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.