The paper is devoted to the evaluation of the hardware resource of computer systems forsolving a computational-expensive problem such as calculation of the probability distributions ofstatistics by the second multiplicity method based on Δ-exact approximations for samples with asize of 320-1280 characters and an alphabet power of 128-256 characters, and with an accuracyof Δ=10-5. The total solution time should not exceed 30 days or 2.592·106 seconds for 24/7 computing.Owing to the use of the properties of the second multiplicity method, the computational complexityof the calculations can be brought to the range of 9.68·1022-1.60·1052 operations with thenumber of tested vectors of 6.50·1023-1.39·1050. The solution of this problem for the specified parametersof samples during the given time requires the hardware resource which cannot be providedby modern computer means such as processors, graphics accelerators, programmable logicintegrated circuits. Therefore, in the paper we analyze the possibilities of promising quantum andphoton technologies for solving the problem with the given parameters. The main advantage ofquantum computer systems is the high speed of calculations for all possible parameter values.However, quantum acceleration will not be achieved to calculate the probability distributions ofstatistics due to the need to check all the obtained solutions. Here, the number of obtained solutionscorresponds to the dimension of the problem. In addition, due to the current developmentlevel of the quantum hardware components, it is impossible to create and use the 120-qubit quantumcomputers for the solution of the considered problem. Photon computers can provide highcomputation speed at low power consumption and require the smallest number of nodes to solvethe considered problem. However, unsolved problems with the physical implementation of efficientmemory elements and the lack of available hardware components make the use of photon computertechnologies impossible for calculation of the probability distributions of statistics in the nearfuture (5-7 years). Therefore, it is most reasonable to use hybrid computer systems containingnodes of different architectures. To solve the problem on various hardware platforms (generalpurposeprocessors, GPUs, FPGAs) and configurations of hybrid computer systems, we suggest touse an architecture independent high-level programming language SET@L. The language combinesthe representation of calculations as sets and collections (based on the alternative set theoryof P. Vopenka), the absolutely parallel form of the problem represented as an information graph,and the paradigm of aspect-oriented programming.
The paper is devoted to the evaluation of the hardware resource of computer systems forsolving a computational-expensive problem such as calculation of the probability distributions ofstatistics by the second multiplicity method based on Δ-exact approximations for samples with asize of 320-1280 characters and an alphabet power of 128-256 characters, and with an accuracyof Δ=10-5. The total solution time should not exceed 30 days or 2.592·106 seconds for 24/7 computing.Owing to the use of the properties of the second multiplicity method, the computational complexityof the calculations can be brought to the range of 9.68·1022-1.60·1052 operations with thenumber of tested vectors of 6.50·1023-1.39·1050. The solution of this problem for the specified parametersof samples during the given time requires the hardware resource which cannot be providedby modern computer means such as processors, graphics accelerators, programmable logicintegrated circuits. Therefore, in the paper we analyze the possibilities of promising quantum andphoton technologies for solving the problem with the given parameters. The main advantage ofquantum computer systems is the high speed of calculations for all possible parameter values.However, quantum acceleration will not be achieved to calculate the probability distributions ofstatistics due to the need to check all the obtained solutions. Here, the number of obtained solutionscorresponds to the dimension of the problem. In addition, due to the current developmentlevel of the quantum hardware components, it is impossible to create and use the 120-qubit quantumcomputers for the solution of the considered problem. Photon computers can provide highcomputation speed at low power consumption and require the smallest number of nodes to solvethe considered problem. However, unsolved problems with the physical implementation of efficientmemory elements and the lack of available hardware components make the use of photon computertechnologies impossible for calculation of the probability distributions of statistics in the nearfuture (5-7 years). Therefore, it is most reasonable to use hybrid computer systems containingnodes of different architectures. To solve the problem on various hardware platforms (generalpurposeprocessors, GPUs, FPGAs) and configurations of hybrid computer systems, we suggest touse an architecture independent high-level programming language SET@L. The language combinesthe representation of calculations as sets and collections (based on the alternative set theoryof P. Vopenka), the absolutely parallel form of the problem represented as an information graph,and the paradigm of aspect-oriented programming.
This paper is devoted to the evaluation of the hardware resources of computer systems for solving a computationally expensive problem such as the calculation of the probability distributions of statistics by the second multiplicity method based on ∆-exact approximations of samples with a size of 320-1280 characters and an alphabet power of 128-256 characters.The accuracy is ∆ = 10 -5 and the total solution time should not exceed 30 days or 2.592 × 10 6 seconds for 24/7 computing.Owing to the use of the properties of the second multiplicity method, the computational complexity of the calculations can be brought within the range of 9.68 × 10 22 -1.60 × 10 52 operations with the number of tested vectors at 6.50 × 10 23 -1.39 × 10 50 .The solution of this problem for the specified parameters of samples during the given time requires hardware resources which cannot be provided by modern computer technology such as processors, graphics accelerators and programmable logic integrated circuits.Therefore, in this paper, we analyze the possibilities of promising quantum and photon technologies for solving the problem with the given parameters.The main advantage of quantum computer systems is the high speed of calculations for all possible parameter values.However, quantum acceleration will not be achieved to calculate the probability distributions of statistics due to the need to check all the obtained solutions.Here, the number of obtained solutions corresponds to the dimension of the problem.In addition, due to the current development level of quantum hardware components, it is impossible to create and use 120 qubit quantum computers for the solution of the considered problem.Photon computers can provide high computation speeds at low power consumptions and require the smallest number of nodes to solve the considered problem.However, unsolved problems with the physical implementation of efficient memory elements and the lack of available hardware components make the use of photon computer technologies impossible for calculating the probability distributions of statistics in the near future (5-7 years).Therefore, it is most reasonable to use hybrid computer systems containing nodes of different architectures.To solve the problem on various hardware platforms (general purpose processors, GPUs and FPGAs) and configurations of hybrid computer systems, we suggest to use the architecture-independent high-level programming language SET@L.The language combines the representation of calculations as sets and collections (based on the alternative set theory of P. Vopenka), the absolutely parallel form of the problem represented as an information graph and the paradigm of aspect-oriented programming.
This article explores the feasibility of using photonic and quantum computing technologies to calculate exact probability distributions of discrete sequence statistics, assuming the existence of working hardware prototypes of computing systems and the development of the required quantum algorithms. The performance evaluation of computing systems based on photonic computing technologies is based on materials from the Sarov Scientific Center for Physics and Microphysics of the Russian Academy of Sciences. The performance of a quantum computing system is assessed by comparing the time it takes to solve a boson sampling problem from a given distribution on a computing system with known performance and the time it takes to solve it on a quantum computing system. To assess the feasibility of using photonic and quantum computing technologies to calculate exact distributions, modern methods for calculating them are considered. These methods are based on solving the type multiplicity equation and a system of linear equations in non-negative integers. Analytical expressions determining the computational complexity of these methods are presented. The values of the boundaries of the parameters of exact distributions accessible for calculation using photonic and quantum computing technologies are determined. A comparison of the obtained results with the results of using multiprocessor computing technologies to calculate exact distributions using various methods is presented. An analysis of the feasibility of using photonic and quantum computing technologies to calculate exact distributions is conducted by comparing the number of parameter pairs that can be calculated for exact distributions with the total number of distribution parameters within the Fisher region, which determines a fivefold increase in sample size over the alphabet size. An analysis of the data on the number of sample parameters shows that with increasing performance of the computing technologies used, the ability to calculate exact distributions increases. However, even with the most powerful quantum technologies, this number does not exceed one-tenth of the total number of exact distributions required for statistical analysis of discrete sequences in alphabets up to 256 characters long
We consider the problem of calculating the approximate value (estimate) of the permanent of a square matrix over the field of real numbers using a photonic quantum computer that sampling bosons from a given distribution. It is pointed out that it is possible to effectively solve this problem for the following three classes of matrices: symmetric matrices which eigenvalues do not exceed 1 in absolute value; orthogonal matrices; doubly stochastic matrices. For the last two classes, we are talking about evaluating the square of the permanent. The mathematical basis for solving the problem is the formula, which represents the permanent of the Hermitian matrix as the mathematical expectation of some random variable which values are equal to the products of the powers of the eigenvalues of the Hermitian matrix. And the corresponding probabilities with which these products are accepted as values of a random variable are also completely determined by the same Hermitian matrix. This circumstance allows using the methods of probability theory in order to solve the problem of permanent estimation.
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.
This is article examines the issue of new conceptual architectures of ultrafast hybrid computing devices based on digital technologies, where the size of an elementary computing device approaches the size of a molecule or even an atom. At this level, the laws of classical physics stop working and quantum laws begin to operate, which for many important dynamic problems have yet to be described theoretically. For such practically significant examples of the use of quantum computers as the training of language models, as well as the analysis of the effectiveness of model training on specified chips and with specified train characteristics (model depth, dataset size, etc.), a new concept for the use of hybrid computing platforms in data centers has emerged. Hybrid computing platforms for data centers represent the integration of various computing resources, including on-premises servers, cloud solutions and virtualized environments. These platforms allow organizations to optimize their computing power, providing flexibility, scalability and costeffectiveness. With the increase in data volumes and the need for cloud services, there is an increase in the creation of data centers. The edge-computing extension, which supports real-time processing at data collection points, matches the potential of quantum computing for revolutionary tasks such as optimization and decision-making. As peripheral systems evolve, the integration of algorithms with quantum technologies can expand their capabilities. This raises pitfalls in evaluating processor performance in hybrid computers, which can vary depending on many factors, including the processor architecture, the types of cores used (for example, high-performance and energy-efficient), as well as the nature of the tasks performed. In this study, a mathematical model of the presented systems is proposed as a combination of combining various concepts that will help to understand and evaluate the performance of hybrid computing, allowing you to optimize the use of resources and improve overall efficiency. Today, there is a growing dependence on hybrid models - mixing local, cloud and peripheral systems, which further emphasizes the need for an infrastructure that accommodates both classical and quantum resources. Quantum computing is increasingly seen as an important part of these hybrid architectures, preparing organizations to meet the new challenges of the advanced computing landscape.
Introduction. Modern information security systems use methods of asymmetric cryptography to transfer encryption keys, which are based on the high computational complexity of factorization of large numbers. Quantum computers (QCs) theoretically make it possible to accelerate the solution of the problem of factorization of numbers in comparison with classical computers and pose a potential threat to information security systems. However, real QCs have a limited number of connections between them and problems with preserving a stable low temperature, which reduces the probability of detecting a global minimum. The joint use of QCs with classical computers based on hybrid cloud services is advisable when the search for the optimal solution by direct methods is a complex problem both in the theoretical sense and in the sense of the required amount of calculations for tasks with specific data. The article proposes a method for improving the accuracy of solving the factorization problem based on multiple minimum search by the method of hardware reverse quantum annealing with a variation of its parameters. The results of numerical experiments for two different QC processors and a hybrid quantum-classical computer by D-Wave are presented, it is shown that the maximum number that can be factorized exclusively by direct annealing is 143, and with a combination of direct and reverse annealing 255. The purpose. Examination of the influence of the parameters of quantum annealing and the corresponding solutions for the adiabatic CC, developed by D-Wave, on the quality of the solution of the factorization problem. To give recommendations for improving the accuracy of solving the factorization problem and increasing the statistical frequency of the appearance of correct pairs of multipliers. Results. Numerical experiments have shown that for the problem of factorization of numbers, the successive application of direct and reverse annealing makes it possible to improve the probability of obtaining the correct pair of multipliers and to more than double the statistical frequency of its occurrence. Quantum annealing modes: pause and quenching reduce the probability of obtaining the correct solution and worsen the statistical frequency of the appearance of correct pairs of multipliers. Conclusions. The use of direct and reverse annealing makes it possible to increase the probability of obtaining the correct solution of the factorization problem for the adiabatic QC of D-Wave. Increasing the calculation time of the problem is justified, since it allows increasing the probability of a correct solution. The use of hybrid quantum-classical computing and cloud services allows factorization for numbers with a bit depth of up to twenty-two bits. Keywords: quantum annealing, factorization of natural numbers, asymmetric shifts, hardening, reverse annealing, combinatorial optimization.