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