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• 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.

• 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.

• A METHOD FOR PLANNING ROBOTIC MOVEMENTS IN COMPLEX CONFLICT ENVIRONMENTS WITH POLYGONAL OBSTACLES

  V.А. Kostyukov

  2026-04-29

  Abstract ▼

  When developing algorithms for real-time robot path planning, the problem of performance limitations of the corresponding classical algorithms arises. This paper considers a method for planning robot movements in a two-dimensional complex conflict environment. For planning in complex environments, a hybrid planning algorithm is proposed, based on a combination and synthesis of the classical cellular decomposition algorithm and a recently proposed algorithm based on the characteristic visibility graph. This algorithm involves a preliminary analysis of the complexity of the obstacle scene, based on the results of which one of the two specified particular algorithms is selected. It is shown that this approach can significantly overcome the limitations of both of these algorithms. A disturbance avoidance method based on the apparatus of characteristic probability functions is described in a compact form, and its relationship with planning methods in complex environments is demonstrated when solving corresponding problems of global optimization of the probability of successful completion of a target trajectory. The developed approach examines the relationship between the probability of successful path completion in a source field and the corresponding risk function. To solve global robot motion planning problems in complex conflict environments, the proposed hybrid algorithm is first proposed for constructing a family of initial curves within the appropriate feasible motion corridors, ignoring sources. A family of local optimization problems is then solved within the feasible motion corridors, taking sources into account. Next, the trajectory with the maximum probability of successful completion or the normalized safe motion function is selected

• HARDWARE-ORIENTED ALGORITHM FOR FAST MULTIPLICATION OF A VECTOR BY A MATRIX KRONECKER PRODUCT

  E.I. Dukhnich, A.G. Chefranov

  2021-02-25

  Abstract ▼

  The article discusses new algorithm to increase the efficiency of the operation of multiplying
  a matrix Kronecker product (KP) by a vector. It is based on the use of the KP properties. This
  operation is widely used in solving problems of processing signals, images, cryptography, etc.,
  where the formation of large matrices with specified properties is performed using small size matrices.
  In this case, matrices with the following properties are used: orthogonal (unitary), invertible,
  involutive. Multiplying an n × n square matrix by a vector has a computational complexity of
  O(n2). Therefore, with an increase in the number of elementary matrix factors, the size of the resulting
  KP matrix and the complexity of multiplying it by a vector grow exponentially. This circumstance
  significantly increases the time for solving applied problems. The aim of the proposed
  work is to construct an algorithm that accelerates the processes of forming the KP and multiplyingthe vector by it. It is proposed to combine the process of multiplication with the process of forming
  the KP. Thus, the KP matrix is not actually calculated explicitly. Instead, the KP factor matrices
  are iteratively multiplied by the vector components in O(nlog2n) time with linear memory complexity.
  The computational scheme with the hypercube topology for the possible hardware implementation
  of the proposed algorithm is presented. It can be easily pipelined. Section 1 presents the definitions
  and properties of the KP used in the synthesis of the proposed algorithm. Section 2 presents
  an example with n = 8 illustrating the proposed algorithm, on the basis of which, in Section
  3, a hardware-oriented structure of its implementation for arbitrary n is proposed.

• ANALYSIS OF ADVANCED COMPUTER TECHNOLOGIES FOR CALCULATION OF EXACT APPROXIMATIONS OF STATISTICS PROBABILITY DISTRIBUTIONS

  А.К. Melnikov, I.I. Levin, А.I. Dordopulo, I.V. Pisarenko

  6-19

  2021-10-05

  Abstract ▼

  In the paper we consider the solution of a computationally expensive problem such as calcu-lation of statistics probability distribution with the help of modern computer technologies. To re-duce computational complexity and to provide a sufficient level of criteria efficiency not less than the specified threshold, we suggest to use Δ-exact approximations. To calculate exact approxima-tions, we use the method of second order, based on solution of a system of linear equations. Owing to this method, it is possible to calculate exact approximations for the maximum values of sample parameters for available computational resource. The most laborious part of the method of second order is the procedure of sequential detection of the vectors of possible solutions and test if the vectors belong to the set of solutions. The system solution set membership test for the vectors of possible solutions is data independent, so the algorithm can be data-parallelized. We give the al-gorithm complexity equation for calculation of exact approximations of statistics probability dis-tributions. Using this equation, we calculated the complexity of modern practical problems for the samples with the parameters (N, n) of the alphabet power and the sample size: (256,1280), (128,640), (128, 320), and (192,3200) for the accuracy of calculations =10-5. The computational complexity is 9.68·1022-1.60·1052 operations, and its average value is about 4.55·1025 operations, the number of tested vectors is 6.50·1023-1.39·1050, and the number of solutions is 4.67·1012-5.60·1025, respectively. The total solution time for clock-round duration of calculations cannot exceed 30 days or 2.592·106 sec. For the obtained complexity evaluation, we analysed abilities of modern cluster computer systems based on general-purpose processors, graphic accelerators, and FPGA-based reconfigurable computer systems. For each technology, we determined the number of computational nodes needed for calculation of exact approximations with the specified parameters during the specified time. We proved that it is impossible to obtain a solution for the required pa-rameters of exact approximations of statistics probability with the help of the reviewed modern computer technologies. In conclusion, we claim that it is necessary to analyse the abilities of ad-vanced computer technologies based of quantum and photonic computers, and also hybrid com-puter systems for calculation of exact approximations of statistics probability distributions with the specified parameters during reasonable time