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• DEVELOPMENT OF MICRO-COMMANDS AND BASIC UNITS OF THE HARDWARE ACCELERATOR OF QUANTUM CALCULATIONS

  S.M. Gushanskiy, V.S. Potapov, Y.M. Borodyansky

  2021-02-13

  Abstract ▼

  At all stages of the development of information technology, much attention has been paid to
  the issues of modeling functioning specialized high-performance computing systems, which make it
  possible to provide the necessary performance indicators in combination with minimized costs of
  software resources and energy consumption. The developed information system, focused on human-
  machine interaction, allows you to clearly see the strengths and weaknesses of the developed
  quantum computing device, to prove the advantages of its use. The developed modeling information
  system is a visual aid for understanding the main methods of interaction between information
  processes and information resources. A number of the most important problems cannot be
  solved 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 solving
  the problem of research and development of a circuit and a simulation technique for a hardware
  accelerator 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 implementation
  of the fundamental components of quantum computing models. The scientific novelty of
  this direction is expressed in the optimization of the quantum computational process. The scientific
  novelty of this area is primarily expressed in the constant updating and supplementing of the field
  of quantum research in a number of areas. The aim of this work is to implement a technique for
  constructing a hardware accelerator. The technical support of the information quantum system
  and processes has been implemented, including new software for the transmission and presentation
  of information. The use of a quantum computing information system differs from its counterparts
  by 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 be
  solved on classical machines in unacceptable time. Due to the fact that the class of NP problems is
  wide, the applicability and significance of the developed method for constructing a modular system
  of quantum computing is beyond doubt.

• QUANTUM DEEP LEARNING OF CONVOLUTIONAL NEURAL NETWORK USING VARIATIONAL QUANTUM CIRCUIT

  S.М. Gushanskiy, V. Е. Buglov

  167-177

  2021-10-05

  Abstract ▼

  Quantum computing in general and quantum deep learning represent a promising field re-lated to the research of modern methods and algorithms of quantum computing used for the pur-pose of teaching and developing new architectures of artificial neural networks. Recently, there has been a trend that research conducted in the field of quantum deep learning is becoming in-creasingly widespread among specialists. This can be explained by the fact that it has been estab-lished that quantum circuits are capable of functioning like artificial neural networks, while demonstrating the best results in solving several tasks, including, for example, the actual task of classifying objects in an image or in a video stream. Thanks to the rapid development of quantum computing in the field of deep learning, optimal solutions have been found for such urgent prob-lems as the vanishing gradient problem, finding a local minimum, improving the efficiency of large-scale parametric machine learning algorithms, eliminating decoherence and quantum er-rors, etc. Within the framework of this work, the process of functioning of a quantum variational scheme is described, its main characteristics are established, and disadvantages are identified. The key features of quantum computing, on which the process of implementing quantum deep learning with the reinforcement of a convolutional neural network is based, are also analyzed. In addition, quantum deep learning of a convolutional neural network has been carried out using a variational quantum scheme, which leads to an increase in the performance of a convolutional neural network in solving the problem of image processing, namely its classification, using a quantum computing environment. The relevance of this article consists in the implementation of a quantum deep learning algorithm with the reinforcement of a convolutional neural network for image processing, as well as the great importance of the subject of this study for the future devel-opment of quantum computing devices that can be used in artificial intelligence systems, etc., which corresponds to the priority direction of the development of domestic science

• DEVELOPMENT OF METHODS OF OPTIMIZATION AND PARALLELIZATION OF COMPUTATIONAL PROCESSES IN QUANTUM ACCELERATORS

  S. M. Gushanskiy, V. S. Potapov, V.I. Bozhich

  2021-08-11

  Abstract ▼

  Recently, there has been a rapid increase in 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 that can actually provide effective performance
  3–4 orders of magnitude higher than any modern computing devices, which will allow solving theabove and others. tasks in real- and accelerated-time scale. This article is devoted to solving the
  problem of research and development of methods for optimizing quantum computing within the
  framework of the application of quantum accelerators. A block diagram of a hardware accelerator
  is proposed to increase the performance of simulated quantum computing. The development of the
  structural diagram of the communication module of the hardware accelerator and the software
  model was carried out. The relevance of these studies lies in mathematical and software modeling
  and implementation of correction codes for correcting several types of quantum errors in the development
  and implementation of quantum algorithms for solving classes of problems of a classical
  nature. The scientific novelty of this direction is expressed in the elimination of one of the disadvantages
  of the quantum computational process. The scientific novelty of this area is primarily
  expressed in the constant updating and supplementation of the field of quantum research in a
  number of areas, and the computer simulation of quantum physical phenomena and features is
  poorly covered in the world.

• IMPLEMENTATION OF A PROBABLE DEEP NEURAL NETWORK DECODER FOR STABILIZER CODES

  S.M. Gushanskiy, V.N. Pukhovsky, V.S. Potapov

  2021-12-24

  Abstract ▼

  Recently, there has been a rapid increase in 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 that can actually provide effective performance
  3–4 orders of magnitude higher than any modern computing devices, which will allow solving the
  above and other tasks in real and accelerated time scale. This work is a study of the influence of
  the environment on a quantum system of qubits and the results of its implementation. A probabilistic
  deep neural network decoder for stabilizer codes has been developed. The issues of error correction
  for a three-bit code without state decoding are analyzed and considered. The relevance of
  these studies lies in mathematical and software modeling and implementation of correction codes
  for correcting several types of quantum errors in the development and implementation of quantum
  algorithms for solving classes of problems of a classical nature. The scientific novelty of this direction
  is expressed in the elimination of one of the disadvantages of the quantum computational
  process. The scientific novelty of this area is primarily expressed in the constant updating and
  supplementation of the field of quantum research in a number of areas.

• DEVELOPMENT AND RESEARCH OF A QUANTUM GRAPH MODEL FOR IMAGE COMPRESSION AND RECONSTRUCTION

  А.N. Samoilov, S.М. Gushanskiy, N.Е. Sergeev, V.S. Potapov

  2024-11-10

  Abstract ▼

  The article discusses in detail the methods and approaches to the application of quantum algorithms
  for solving optimization and image processing problems. Particular attention is paid to quantum approximate
  optimization (QAO) and the use of quantum networks for data compression and reconstruction problems.
  QAO is a hybrid algorithm that combines quantum and classical computational processes, allowing
  one to efficiently solve complex combinatorial problems. QAO is based on parameterized unitary operations
  that are optimized during iterations. This approach makes it possible to consider the unique features
  of the quantum nature of information, which in some cases allows achieving higher performance than
  when using exclusively classical methods. In the process of implementing QAO, one of the main obstacles
  remains the problem of noise, which can arise, for example, when using CNOT gates. The article discusses
  various strategies for reducing the noise level, which is an important task for ensuring the stability and
  improving the accuracy of quantum algorithms. For example, methods for isolating individual operations
  and correcting errors are considered, which allows one to minimize the impact of noise on the calculation
  results and improve the accuracy of quantum optimization. The authors also propose a graph interpretation
  of quantum models based on the use of tensor networks. This approach allows for efficient simplification
  of computational graphs, thereby optimizing the resources required to perform complex quantum
  operations. This method also demonstrates high efficiency in image compression and restoration tasks,
  which opens up new prospects for the application of quantum networks in data processing. The article
  describes the structure of quantum networks, including multilayer quantum gates, which allow for deeper
  and more detailed image processing, providing both efficient compression and high-quality data restoration.
  An analysis of various types of quantum gates, such as Hadamard, Pauli-X, Pauli-Y, and T-gates,
  was also conducted. These gates play a key role in the efficiency of quantum algorithms, since each of
  them contributes to quantum dynamics and the way quantum states are manipulated

• CHARACTERISTICS OF QUANTUM CIRCUITS WITH FUNCTIONAL CONFIGURATIONS OF QUBITS

  S.M. Gushanskiy, V.S. Potapov

  2024-01-05

  Abstract ▼

  The paper is an exploration of a new approach to the systematic analysis and classification
  of quantum circuits based on the functional configuration of qubits. The article examines in detail
  the role of elementary gates in changing the elements of the state vector and highlights the importance
  of functional configurations of qubits in the collective modification of quantum states.
  The main aspects covered in the article include the characterization of quantum circuits with functional
  configurations of qubits, analysis of the impact of elementary gates on the state of a quantum
  vector, and determination of the number of possible types of functional configurations.
  The results of the study could have important implications for optimizing quantum circuits and
  improving our understanding of their general properties. A qubit functional configuration is a
  mathematical structure that can collectively classify the properties and behavior of quantum circuits.
  The development of quantum algorithms with efficient quantum circuits has been a central
  part of quantum computing, which has seen enormous progress both theoretically and experimentally
  over the past 30 years. The paper makes a contribution to the field of quantum computing by
  providing a systematic approach to classify and analyze quantum circuits based on their functional
  qubit configurations. Quantum algorithms are an innovative class of algorithms based on the
  principles of quantum mechanics and using qubits instead of classical bits to process information.
  Unlike classical algorithms, which operate on bits that take on the values 0 or 1, quantum algorithms
  can use the principles of quantum superposition and quantum interaction, which allows
  them to perform many calculations simultaneously. One of the key advantages of quantum algorithms
  is their ability to solve certain problems much more efficiently than classical algorithms.
  However, the design and implementation of quantum algorithms pose significant technical and
  algorithmic challenges, such as managing quantum states, minimizing errors, and creating robust
  quantum gates. Despite these challenges, quantum algorithms offer promising opportunities to
  revolutionize computing and solve problems that have traditionally been too complex for classical
  computers

• RESEARCH AND DEVELOPMENT OF DEPTH OPTIMIZED CIRCUITS IN QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM

  S.M. Gushanskiy, V.S. Potapov, V.I. Bozhich

  2023-12-11

  Abstract ▼

  One of the main challenges faced by researchers in the field of quantum computing is the problem
  of noise in quantum systems. Noise can significantly limit the performance of quantum algorithms.
  It is in this context that our research, aimed at the development and optimization of quantum
  algorithms with a focus on depth, is updated. The depth of quantum circuits is one of the critical parameters
  in the development of quantum algorithms. Optimized circuits with improved depth have the potential to significantly reduce the impact of noise, which in turn should lead to improved efficiency.
  We aim to provide solutions that not only address technical constraints, but also provide practical
  results for quantum computing in the context of optimization problems. This study analyzes the use of
  a quantum approximate optimization algorithm for solving complex combinatorial optimization
  problems. However, in the process of using this algorithm we encounter a serious limitation – noise
  in the quantum system, which significantly reduces its efficiency. To overcome the influence of noise
  and improve the efficiency of quantum algorithms, several methods have been proposed. This paper
  presents a greedy heuristic algorithm aimed at reducing the impact of noise. The main goal of this
  algorithm is to find a spanning tree of minimum height. This, in turn, reduces the overall depth of
  quantum circuits and minimizes the number of CNOT gates, which is key to optimizing quantum
  computing. Through numerical analysis, it was demonstrated that the proposed greedy heuristic
  algorithm is capable of significantly increasing the probability of successful completion of each iteration
  in the problem of finding the maximum cut in a graph by 10 times. Moreover, the study confirms
  that the average depth of the quantum circuit generated by the proposed heuristic algorithm is still
  linearly dependent on the size of the input data, but the slope of this linear dependence is reduced
  from 1 to 0.11 by using the proposed method.

• DEVELOPMENT AND STUDY OF A CONTROL MODEL BASED ON NOISE-RESISTANT QUANTUM COMPUTING, SUPPRESSION AND CORRECTION OF ERRORS IN QUANTUM COMPUTING

  S.М. Gushanskiy, V.S. Potapov

  2023-10-23

  Abstract ▼

  In recent years, quantum information systems have attracted increasing attention of researchers
  in the field of computer science and physics. However, the introduction and practical
  application of quantum computing is limited by the influence of noise and errors that occur in
  quantum systems. To implement effective control and improve the reliability of quantum information
  systems, it is necessary to develop methods that can suppress and correct errors in the
  process of quantum computing. The purpose of this work is to develop and study a control model
  based on noise-immune quantum computing, as well as methods for suppressing and correcting
  errors in quantum computing. The paper proposes a combination of different approaches, including
  the use of error correction codes, noise suppression algorithms, and methods for optimal control
  of quantum information systems. In the course of the study, a control model was developed
  that allows efficient processing of information in quantum systems, taking into account the presence
  of noise and errors. Experiments were carried out using real quantum devices to evaluate the
  effectiveness of the proposed model. The experimental results show that the developed method can
  significantly improve the reliability and accuracy of quantum computing. The proposed control
  model based on noise-immune quantum computing and methods for suppressing and correcting
  errors represent a significant contribution to the development of quantum information systems.
  Further development and optimization of the proposed approach can lead to the creation of more
  reliable and efficient quantum systems capable of solving complex computational problems.

• STUDY OF A QUANTUM COMPUTING SYSTEM AND IMPLEMENTATION OF A QUANTUM CORE ON FPGA

  S.M. Gushanskiy, V.S. Potapov

  2023-02-17

  Abstract ▼

  The quantum core method is one of the most important methods in quantum machine learning.
  However, the number of features used for quantum nuclei is limited to a few dozen features.
  The block product state structure is used as a quantum feature map and the implementation of
  programmable gate matrices is demonstrated. The relevance of these studies lies in the mathematical
  and software modeling and implementation of a quantum computing system as part of the
  development of the implementation of a quantum core on FPGA for solving classes of problems of
  a classical nature. The scientific novelty of this research area is the development of a hybrid simulator
  of the quantum cores of a central processing unit (CPU) and a programmable logic integrated
  circuit (FPGA) several orders of magnitude faster than a conventional quantum computing
  simulator. This joint development of the implemented quantum core and its efficient FPGA implementation allowed numerical simulation of the quantum core based on gates in terms of input
  features, up to 780-dimensional features using 4000 samples. We applied the quantum kernel to
  image classification problems using the Fashion-MNIST dataset and showed that the quantum
  kernel is comparable to Gaussian kernels with optimized throughput. The analysis of the work in
  this field has shown that a new qualitative level has now been reached, opening up promising opportunities
  for the implementation of multi-qubit quantum computing. The prospects for implementation
  and development are connected not only with technological capabilities, but also with solving
  the issues of building effective quantum systems for solving actual mathematical problems,
  cryptography problems and control (optimization) problems.

• DEVELOPMENT OF CORRECTION CODES FOR CORRECTING SEVERAL KINDS OF QUANTUM ERRORS

  S.M. Gushanskiy, V. S. Potapov, V.I. Bozhich

  2020-10-11

  Abstract ▼

  Recently, there has been a rapid increase in interest in quantum computers. Their work is
  based on the use of quantum-mechanical phenomena such as superposition and entanglement for
  computing input data into output data that can actually provide effective performance 3 to 4 orders of
  magnitude higher than any modern computing devices, which will solve the above and others tasks in
  a natural and accelerated time scale. This article is devoted to solving the problem of research and
  development of corrective codes for correcting several types of quantum errors that appear during
  computational processes in quantum algorithms and models of quantum computing devices. The aim
  of the work is to study existing methods for correcting various types and types of quantum errors and
  to create a 3-qubit corrective code for quantum error correction. The work touches upon the tasks of
  research and development of the functioning methods of quantum circuits and models of quantum
  computing devices. The relevance of these studies lies in the mathematical and software modeling
  and implementation of corrective codes for correcting several types of quantum errors as part of the
  development and implementation of quantum algorithms for solving classes of classical problems.
  The scientific novelty of this area is expressed in the exclusion of one of the shortcomings of the
  quantum computing process. The scientific novelty of this area is primarily expressed in the constant
  updating and addition of the field of quantum research in a number of areas, and computer simulation of quantum physical phenomena and features is poorly illuminated in the world. The aim of the work is computer simulation of a quantum computing process using the method of correcting
  phase types of errors, which allows one to evaluate the own phase of a unitary gate that has
  gained access to the quantum state in proportion to its own vector.