Article 6317

Title of the article

TESTING OF ANALOG AND QUANTUM ORACLES OF LINEAR COMPUTATIONAL COMPLEXITY,
PREDICTING THE VALUES OF THE CORRELATION COEFFICIENT ON A SMALL SAMPLE IN 32 EXPERIMENTS 

Authors

Volchikhin Vladimir Ivanovich, Doctor of engineering sciences, professor, President of Penza State University (40 Krasnaya street, Penza, Russia), president@pnzgu.ru,
Ivanov Aleksandr Ivanovich, Doctor of engineering sciences, associate professor, head of the laboratory of biometric and neural network technologies, Penza Research Institute of Electrical Engineering (9 Sovetskaya street, Penza, Russia), ivan@pniei.penza.ru, aosv68@bk.ru
Serikov Andrey Vasil'evich, Head of department, "Rubin" enterprise (2 Baydukova street, Penza, Russia), aosv68@bk.ru
Serikova Julia Igorevna, Master’s degree student, Penza State University (40 Krasnaya street, Penza, Russia), julia-ska@yandex.ru

Index UDK

519.24; 53; 57.017

DOI

10.21685/2072-3059-2017-3-6

Abstract

Background. The aim of the paper is to reduce errors in calculating correlation coefficients for small test samples.
Materials and methods. Simulation means are used to obtain continuous and discrete functions of the distribution density of correlation coefficients. We consider a mathematical correlation molecule that generates a spectrum of 16 states at the output.
The article describes the general scheme for synthesizing the analog oracle’s form and the quantum oracle’s form, which predicts the values of the correlation coefficients for a small sample of 32 experiments.
Results. The oracle’s analog version allows to reduce the standard deviation of calculation errors to 11.6 %, which is equivalent to an increase in the number of experiments from 32 to 39. The quantum version with linear computational complexity allows reducing the standard deviation of the error to 85 %, which is equivalent to increasing the sample sizes from 32 to 109 experiments.
Conclusions. Quantum oracles constructed using correlation mathematical molecules are much more efficient than analog forms of oracles. Presumably, the transition from quantum oracles with linear computational complexity to quantum oracles with quadratic computational complexity will additionally reduce the error in calculating the correlation coefficients. There is a specific regularization of calculations, allowing to exchange computer’s resources for an equivalent test sample volume.

Key words

correlation coefficient, quantum superposition, correlation molecule, discrete spectrum of states, statistical analysis of small samples 

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References

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Дата создания: 06.02.2018 10:35
Дата обновления: 26.02.2018 15:41