In the past few decades the problem of creating quantum computer is one of the most important. Quantum computer uses the quantum mechanics such as quantum parallelism and quantum entanglement. Using this mechanisms quantum computer is able to solve some of the problems of NP-class in polynomial time. In our days the prototypes of such class of devices are created, but they cant be used for effective solving of the planned problems because of difficulties of realization. However, mathematical apparatus that describes the behavior of quantum particles using wave function exists. This apparatus allows creating algorithms that can be effectively solved only on quantum computer. Hence its a problem of investigation of effectiveness of new quantum algorithms. The only option is modeling quantum system on classical devices. But the quantum system cant be modeled effectively on classical devices, hence its suggested to use methodic of accelerating of modeling of quantum computing.
In the past few decades the problem of creating quantum computer is one of the most important. Quantum computer uses the quantum mechanics such as quantum parallelism and quantum entanglement. Using this mechanisms quantum computer is able to solve some of the problems of NP-class in polynomial time. In our days the prototypes of such class of devices are created, but they cant be used for effective solving of the planned problems because of difficulties of realization. However, mathematical apparatus that describes the behavior of quantum particles using wave function exists. This apparatus allows creating algorithms that can be effectively solved only on quantum computer. Hence its a problem of investigation of effectiveness of new quantum algorithms. The only option is modeling quantum system on classical devices. But the quantum system cant be modeled effectively on classical devices, hence its suggested to use methodic of accelerating of modeling of quantum computing.
At all stages of the development of information technology, much attention has been paid tothe issues of modeling functioning specialized high-performance computing systems, which make itpossible to provide the necessary performance indicators in combination with minimized costs ofsoftware resources and energy consumption. The developed information system, focused on human-machine interaction, allows you to clearly see the strengths and weaknesses of the developedquantum computing device, to prove the advantages of its use. The developed modeling informationsystem is a visual aid for understanding the main methods of interaction between informationprocesses and information resources. A number of the most important problems cannot besolved using classical computers, including classical supercomputers, in a reasonable time. Recently,there has been a surge in interest in quantum computers. This article is devoted to solvingthe problem of research and development of a circuit and a simulation technique for a hardwareaccelerator of quantum computing. The work touches upon the problems of research and development of methods for the functioning of quantum circuits and models of quantum computing devices.The relevance of these studies lies in the mathematical and software modeling and implementationof the fundamental components of quantum computing models. The scientific novelty ofthis direction is expressed in the optimization of the quantum computational process. The scientificnovelty of this area is primarily expressed in the constant updating and supplementing of the fieldof quantum research in a number of areas. The aim of this work is to implement a technique forconstructing a hardware accelerator. The technical support of the information quantum systemand processes has been implemented, including new software for the transmission and presentationof information. The use of a quantum computing information system differs from its counterpartsby a significant increase in the speed of solving computational problems and, most importantly,by an exponential increase in the speed of solving NP-complete problems that can besolved on classical machines in unacceptable time. Due to the fact that the class of NP problems iswide, the applicability and significance of the developed method for constructing a modular systemof quantum computing is beyond doubt.
Recently, there has been a rapid increase interest in quantum computers. Their work is based on the use of quantum-mechanical phenomena such as superposition and entanglement for computing to transform input data into outputs, which can actually provide effective performance 3-4 orders of magnitude higher than any modern computing devices. In the past few decades, there has been an acute problem of creating a quantum computer that uses quantum mechanical effects for computations. Currently, there are prototypes of devices of this class, but it is not yet possible to achieve an effective solution to the planned tasks with their help due to a number of difficulties in implementation. However, there is a mathematical apparatus that describes the behavior of quantum particles using a wave function. Hence, it becomes possible to simulate quantum computations on the classical architecture and check the reliability of algorithms belonging to the NP class, which are theoretically executed on a quantum computer in polynomial time and which cannot be solved on classical computers within an acceptable time frame. Effectively simulate the operation of a quantum system on devices with classical architecture is impossible, it remains to propose methods for acceleration of quantum computing on classical systems.
A hardware approach for the quantum computing modeling was considered. A common mathematical model of the quantum computer was described; a methodic of mathematical modeling of the quantum computing was shown. During the mathematical methodic description the most resource-intensive parts of the model are allocated. Considered questions connected with data parallelizing with a hardware accelerator, which is used for quantum computer modeling. A common scheme of the accelerator’s work algorithm was shown. Suggested more compact data format for accelerator implementation, that will reduce time costs spent by elementary arithmetic operations. Proposed the use of the optimization algorithm for data minimization during the calculations in the phase of transforming model of quantum register with quantum gates in quantum computer simulators. Shown results of optimization algorithm execution and compared results with classic mathematical approach.
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.
This article discusses the principles of quantum computing simulation using hardware approach. We describe a general mathematical model of a quantum computer; we show the method of mathematical modeling of quantum computation with optimization and a scheme of a hardware processing core in a quantum computing accelerator. The article gives a method of assessment of increasing productivity in the simulation of quantum computations using computing hardware core. The problems associated with the parallelization of computations on a hardware accelerator, simulating quantum computing were analyzed. The work lists the results of comparison of software and hardware simulation, as well as the dependence of the temporal evaluation of the number of qubits and parallel ALU in the computer-hardware accelerator
В статье рассматриваются принципы квантовых вычислений на основе спиновых состояний. Анализируются фундаментальные принципы квантовой физики, такие как суперпозиция, запутанность и корпускулярно-волновой дуализм. Описаны математические модели кубитов в сфере Блоха, уравнение Шрёдингера и процесс коллапса волновой функции при измерении. Показана роль спиновой запутанности в реализации квантовых алгоритмов. Проведен анализ возможностей применения квантовых алгоритмов в области криптографии, моделирования сложных систем и др. The article examines the principles of quantum computing based on spin states. It analyzes the fundamental principles of quantum physics, such as superposition, entanglement, and particle-wave duality. Mathematical models of qubits on the Bloch sphere, the Schrödinger equation, and the wave function collapse during measurement are described. The role of spin entanglement in implementing quantum algorithms is demonstrated. The possibilities of using quantum algorithms in cryptography, complex systems modeling, and optimization.