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 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.
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 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.
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.
The technology of Quantum Computing (QC) is continuously evolving, as researchers explore new technologies and the public gains access to quantum computers with an increasing number of qubits. In addition, the research community and industry are increasingly interested in the potential use, application, and contribution of QCs to large-scale problems in the real world as a result of this technological enhancement. QCs operations are based on quantum mechanics, and their special properties are mainly exploited to solve computationally intensive problems in polynomial time, problems that are commonly unsolvable, even by High-Performance Computing systems (HPCs) in a feasible time. However, since QCs cannot perform as general-purpose computing machines, alternative computational approaches aiming to boost further their enormous computing abilities are requested, and their combination as an additional computing resource to HPC systems is considered as one of the most promising ones. In the proposed hybrid HPCs, the Quantum Processing Units (QPUs), similar to GPUs and CPUs, target specific problems that, through Quantum Algorithms, can exploit quantum properties like quantum entanglement and superposition to achieve substantial performance gains from the HPC point of view. This interconnection between classical HPC systems and QCs towards the creation of Hybrid Quantum-Classical computing systems is neither straightforward nor standardized while crucial for unlocking the real potential of QCs and achieving real performance improvements. The interconnection between the classical and quantum systems can be performed in the hardware, software (system), or application layer. In this study, a concise overview of the existing architectures for the interconnection interface between HPCs and QCs is provided, focusing mainly on hardware approaches that enable effective hybrid quantum-classical operation.
Quantum computing has the potential to revolutionise multiple fields by solving complex problems that cannot be solved in reasonable time with current classical computers. Nevertheless, the development of quantum computers is still in its early stages and the available systems have still very limited resources. As such, currently, the most practical way to develop and test quantum algorithms is to use classical simulators of quantum computers. In addition, the development of new quantum computers and their components also depends on simulations. Given the characteristics of a quantum computer, their simulation is a very demanding application in terms of both computation and memory. As such, simulations do not scale well in current classical systems. Thus different optimisation and approximation techniques need to be applied at different levels. This review provides an overview of the components of a quantum computer, the levels at which these components and the whole quantum computer can be simulated, and an in-depth analysis of different state-of-the-art acceleration approaches. Besides the optimisations that can be performed at the algorithmic level, this review presents the most promising hardware-aware optimisations and future directions that can be explored for improving the performance and scalability of the simulations.