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• STUDY OF POSSIBILITIES OF USING PHOTONIC AND QUANTUM COMPUTING TECHNOLOGIES TO CALCULATE EXACT PROBABILITY DISTRIBUTIONS OF STATISTIC VALUES FROM FINITE DISCRETE SEQUENCES

  А.К. Melnikov

  121-136

  2025-12-30

  Abstract ▼

  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

• FLOATING–POINT ADDER IN DIGITAL PHOTONIC COMPUTING SYSTEMS

  D.А. Sorokin , I.I. Levin

  168-178

  2025-11-10

  Abstract ▼

  Within the structural computation paradigm proposed by the authors, digital photonic computing systems are expected to employ sequential data processing, which allows for the minimization of operand duty cycle gaps when data is supplied from external memory or other electronic sources to the photonic device. This becomes feasible when the processing time per operand does not exceed the number of clock cycles corresponding to the operand’s bit width. Moreover, sequential digit–wise processing significantly reduces hardware costs associated with dataflow synchronization. The elimination of duty cycle gaps and reduction in structural overhead can substantially enhance the efficiency of digital photonic computing systems relative to their electronic counterparts. However, to enable photonic computational architectures capable of solving complex and computation–intensive problems in domains such as mathematical physics, linear algebra, neural network processing, and others, it is necessary to implement core arithmetic functions in floating–point format. Most of these functions are built around elementary integer addition. In binary systems with sequential processing in least–significant–digit–first order, integer adders are unable to begin producing results until all bits have been processed and carry propagation is complete, thereby doubling the operand duty cycle and increasing latency. To address these issues, this paper proposes the use of a quaternary signed–digit number representation with operands processed in most–significant–digit–first order. This representation enables immediate transmission of the most significant digits of the result to downstream processing units, without waiting for the completion of lower–order digit computation. This paper addresses the design of all components of the signed–digit floating–point adder: the exponent difference unit, the mantissa denormalization unit for the operand with the smaller exponent, the mantissa adder, the mantissa normalization unit for the result, and the exponent correction unit. Operational algorithms for these units are presented. The performance of the proposed signed–digit adder has been evaluated on a prototype implemented in a digital photonic logic framework on the reconfigurable “Terzius” computing platform. It is demonstrated that, due to the high clock frequency achievable by digital photonic computing devices, their performance can exceed that of microelectronic devices by nearly two orders of decimal scale.

• STUDY OF THE PROPAGATION OF LIGHT WITH A WAVELENGTH OF 1.3 ΜM IN TWO-DIMENSIONAL GaAs-BASED PHOTONIC CRYSTALS WITH A WAVEGUIDE–MICRORESONATOR CONFIGURATION

  Maximilian Pleninger , S.V. Balakirev , М.S. Solodovnik

  133-142

  2025-11-10

  Abstract ▼

  Photon crystals are semiconductor structures characterized by a periodic variation of dielectric permittivity in space with a period comparable to the wavelength of electromagnetic radiation. Interest in these structures is driven both by the importance of fundamental research into light-matter interactions and by the prospects for applying photonic crystals in optical integrated circuits and next-generation optoelectronic components. This paper presents the results of a study on the propagation patterns of electromagnetic radiation with a wavelength of 1.3 μm in two-dimensional photonic crystals based on gallium arsenide (GaAs). The research is based on a numerical model using the Comsol Multiphysics 6.1 software package and includes an analysis of the electric field intensity distribution in complex photonic crystal structures consisting of a waveguide coupled to a hexagonal microcavity (microresonator) with various geometric parameters. The influence of a deliberately introduced defect radius in the waveguide region on the efficiency of radiation transmission into the resonator area also analyzed. For numerical analysis, methods for simulating the propagation of transverse electric waves in two-dimensional photonic crystals with a hexagonal lattice of air holes employed. The geometric parameters of the basic photonic crystal structure remained constant: the air hole radius was 209 nm, and the lattice period was 520 nm. The waveguide was formed by removing one row of air holes, while the microresonator was created by forming a hexagonal air cavity near the waveguide. To enhance the coupling efficiency between the waveguide and resonator, a defect in the form of an air hole with a variable radius was introduced into the structure. Analysis showed that maximum localization of the electromagnetic field in a hexagonal cavity with a diameter of 1.65 μm was achieved when the cavity was positioned two rows of air holes away from the waveguide. Increasing this distance resulted in a reduction of field intensity within the resonator. Introduction of the defect significantly enhanced energy transfer efficiency from the waveguide to the resonator. The highest integral electric field intensity in the resonator region was observed when the defect radius ranged from 246 to 290 nm. The obtained data can be used in the development of compact optical devices such as lasers, modulators, and switches based on photonic crystals

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

  А.К. Melnikov, I.I. Levin, А.I. Dordopulo, L.M. Slasten

  2022-11-01

  Abstract ▼

  The paper is devoted to the evaluation of the hardware resource of computer systems for
  solving a computational-expensive problem such as calculation of the probability distributions of
  statistics by the second multiplicity method based on Δ-exact approximations for samples with a
  size of 320-1280 characters and an alphabet power of 128-256 characters, and with an accuracy
  of 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 complexity
  of the calculations can be brought to the range of 9.68·1022-1.60·1052 operations with the
  number of tested vectors of 6.50·1023-1.39·1050. The solution of this problem for the specified parameters
  of samples during the given time requires the hardware resource which cannot be provided
  by modern computer means such as processors, graphics accelerators, programmable logic
  integrated circuits. Therefore, in the 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 the quantum hardware components, it is impossible to create and use the 120-qubit quantum
  computers for the solution of the considered problem. Photon computers can provide high
  computation speed at low power consumption 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 calculation of 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 (generalpurpose
  processors, GPUs, FPGAs) and configurations of hybrid computer systems, we suggest to
  use an 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.