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Международный журнал Программные продукты и системы

Программный эмулятор квантовых алгоритмов для эффективного моделирования на персональном компьютере

Sergey Victorovich Ulyanov, Sergey Victorovich Ulyanov

Published Mar 16, 2024• 0 citations
Publisher

Abstract

A quantum software engineering platform includes quantum computing methods, a quantum algorithm theory and quantum programming.These areas develop according to a technological structure of nanotechnology development for hardware design of various configurations.In about 10 to 30 years we expect the appearing of an industrial quantum computer for real software engineering; this fact is due to overcoming a number of technological difficulties in implementing hardware, as well as the fundamental difficulty of eliminating decoherence physical phenomenon and correcting errors in quantum computers in near future.A key question in quantum computing is searching for quantum algorithms that potentially have a significant advantage and supremacy over classical algorithms for problems of practical interest.Therefore, currently, an approach is being developed to create quantum algorithm structures for quantum simulators with the possibility of effective implementation on classical architecture computers.This paper proposes an effective modelling method with information analysis of quantum search and decision-making algorithm structures in order to eliminate redundancy in practical implementation of a simulator on a classical structure computer.As an example, we demonstrate the method of modeling Grover's quantum search algorithm with stopping the search for a good solution based on the Shannon information entropy minimum principle.There are modeling examples to demonstrate the effectiveness of the developed approach in quantum software engineering and intelligent control robotics.

DOI
10.15827/0236-235x.145.005-017

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A quantum software engineering platform includes quantum computing methods, a quantum algorithm theory and quantum programming.These areas develop according to a technological structure of nanotechnology development for hardware design of various configurations.In about 10 to 30 years we expect the appearing of an industrial quantum computer for real software engineering; this fact is due to overcoming a number of technological difficulties in implementing hardware, as well as the fundamental difficulty of eliminating decoherence physical phenomenon and correcting errors in quantum computers in near future.A key question in quantum computing is searching for quantum algorithms that potentially have a significant advantage and supremacy over classical algorithms for problems of practical interest.Therefore, currently, an approach is being developed to create quantum algorithm structures for quantum simulators with the possibility of effective implementation on classical architecture computers.This paper proposes an effective modelling method with information analysis of quantum search and decision-making algorithm structures in order to eliminate redundancy in practical implementation of a simulator on a classical structure computer.As an example, we demonstrate the method of modeling Grover's quantum search algorithm with stopping the search for a good solution based on the Shannon information entropy minimum principle.There are modeling examples to demonstrate the effectiveness of the developed approach in quantum software engineering and intelligent control robotics.
Principles and methodologies of quantum algorithmic gates design for master course and PhD students in computer science, control engineering and intelligent robotics described. The possibilities of quantum algorithmic gates simulation on classical computers discussed. Applications of quantum gate of nanotechnology in intelligent quantum control introduced. Anew approach to a circuit implementation design of quantum algorithm gates for fast quantum massive parallel computing presented. The main attention focused on the development of design method of fast quantum algorithm operators as superposition, entanglement and interference, which are in general time-consuming operations due to the number of products that have performed. SW & HW support sophisticated smart toolkit of supercomputing accelerator of quantum algorithm simulation on small quantum programmable computer algorithm gate (that can program in SW to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates) described. As example, the method for performing Grover’s interference operator without product operations introduced. The background of developed information technology is the "Quantum / Soft Computing Optimizer" (QSCOptKBTM) SW based on soft and quantum computational intelligence toolkit.
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some sense, give a function to QA to analyze and QA returns its property as an answer without quantitative computing. QA studies qualitative properties of the functions. The core of any QA is a set of unitary quantum operators or quantum gates. In practical representation, quantum gate is a unitary matrix with particular structure. The size of this matrix grows exponentially with an increase in the number of inputs, which significantly limits the QA simulation on a classical computer with von Neumann architecture. Quantum search algorithm (QSA) - models apply for the solution of computer science problems as searching in unstructured data base, quantum cryptography, engineering tasks, control system design, robotics, smart controllers, etc. Grovers algorithm is explained in details along with implementations on a local computer simulator. The presented article describes a practical approach to modeling one of the most famous QA on classical computers, the Grover algorithm.
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators.Input to QA in this case is always the same.Output of QA says which problem coded.In some sense, give a function to QA to analyze and QA returns its property as an answer without quantitative computing.QA studies qualitative properties of the functions.The core of any QA is a set of unitary quantum operators or quantum gates.In practical representation, quantum gate is a unitary matrix with particular structure.The size of this matrix grows exponentially with an increase in the number of inputs, which significantly limits the QA simulation on a classical computer with von Neumann architecture.Quantum search algorithm (QSA)models apply for the solution of computer science problems as searching in unstructured data base, quantum cryptography, engineering tasks, control system design, robotics, smart controllers, etc. Grover's algorithm is explained in details along with implementations on a local computer simulator.The presented article describes a practical approach to modeling one of the most famous QA on classical computers, the Grover algorithm.
The second (quantum computing algorithms and HW-computers) and third quantum (quantum programming and SW-engineering and quantum “powerful” computing AI) revolutions have led to the necessity in developing of intelligent SW/HW platform (strong quantum computational AI) of industrial quantum technologies for mega - science projects “Industry 5.0 / 6.0”. This fact, in turn, has raised the big challenge of training a new generation of quantum engineering staff in the fields of quantum end-to-end IT, quantum software engineering and quantum intelligent control. The creation of an appropriate software-algorithmic platform and hardware support in view of a quantum computer for industrial development required a radical revision of the foundations of educational processes for quantum engineering, the creation of a new technological structure and mathematical / physical / technical background in dynamically developing areas of application of quantum end-to-end IT. The lack of teaching staff and objective assessments of the necessity of industry and science for quantum engineering personnel only increased the difficulties in the development of quantum engineering. There is a certain mathematical maturity required to understand the quantum mechanics of finite dimensional systems. We review only the basics here and this is mostly to familiarize the reader with the notation used for the remainder of this Introduction.
A new approach to a circuit implementation design of quantum algorithmic gates for the realization of quantum massive parallel computing presented. The main attention focused on the development of design method of fast quantum algorithm operators as superposition, entanglement and interference which are in general time-consuming operations due to the number of products that have to be performed. SW&HW support toolkit of supercomputing accelerator of quantum algorithm simulation on classical computer described. The method for performing Grover's interference without product operations introduced. New quantum genetic and quantum fuzzy inference algorithm gate design for intelligent robotic control considered. Quantum software engineering supremacy on Benchmarks demonstrated.
In recent years, quantum computing has attracted considerable attention due to its potential to solve complex problems inaccessible to classical computers. One of the priority areas of application of quantum algorithms is cryptographic analysis, since quantum computers are able to effectively crack widely used cryptosystems such as RSA and ECC. However, the development of quantum algorithms faces a number of difficulties related to optimizing their structure and parameters. This study examines the application of machine learning (ML) methods to improve the efficiency of quantum algorithms in cryptographic analysis tasks. To achieve this goal, hybrid quantum-classical approaches were used, combining the advantages of quantum computing and machine learning. Learning algorithms with and without a teacher were used to automatically adjust the parameters of quantum algorithms, including noise reduction and optimization parameters. The research was based on simulation of quantum operations on simulators and testing on real quantum processors. The use of machine learning methods made it possible to reduce the execution time of quantum algorithms by 20-30% while maintaining the accuracy of the result. In addition, learning optimization has reduced the need for quantum resources, such as the number of gates, which opens up opportunities for performing complex tasks on quantum devices with limited power. The use of such approaches has been demonstrated by the example of cryptographic analysis of the Shor algorithm. The results obtained show the effectiveness of integrating machine learning methods into the process of developing quantum algorithms. This opens up prospects for further research aimed at creating more powerful tools for cryptanalysis and other tasks. The study proves the feasibility of using machine learning to optimize quantum algorithms, improving their performance and expanding the scope of possible applications, including cryptographic analysis. В последние годы квантовые вычисления привлекают значительное внимание из-за своего потенциала решения сложных задач, недоступных классическим компьютерам. Одной из приоритетных областей применения квантовых алгоритмов является криптографический анализ, поскольку квантовые компьютеры способны эффективно взламывать такие широко используемые криптосистемы, как RSA и ECC. Однако разработка квантовых алгоритмов сталкивается с рядом трудностей, связанных с оптимизацией их структуры и параметров. В данном исследовании рассматривается применение методов машинного обучения (МО) для повышения эффективности квантовых алгоритмов в задачах криптографического анализа. Для достижения этой цели были использованы гибридные квантово-классические подходы, объединяющие преимущества квантовых вычислений и машинного обучения. Для автоматической настройки параметров квантовых алгоритмов, включая параметры шумоподавления и оптимизации, использовались алгоритмы обучения с учителем и без него. Исследование проводилось на основе моделирования квантовых операций на симуляторах и тестирования на реальных квантовых процессорах. Использование методов машинного обучения позволило сократить время выполнения квантовых алгоритмов на 20-30% при сохранении точности результата. Кроме того, оптимизация обучения снизила потребность в квантовых ресурсах, таких как количество вентилей, что открывает возможности для выполнения сложных задач на квантовых устройствах с ограниченной мощностью. Использование таких подходов продемонстрировано на примере криптографического анализа алгоритма Шора. Полученные результаты показывают эффективность интеграции методов машинного обучения в процесс разработки квантовых алгоритмов. Это открывает перспективы для дальнейших исследований, направленных на создание более мощных инструментов для криптоанализа и других задач. Исследование доказывает целесообразность использования машинного обучения для оптимизации квантовых алгоритмов, повышения их производительности и расширения сферы возможных приложений, включая криптографический анализ.