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Statement of the problem of assessing instability of passive quantum frequency standards in the presence of an error from the interaction

Олексій Нарєжній, Tetiana Grinenko, І.Д. Горбенко

Published Sep 24, 2021• 0 citations
Publisher

Abstract

Construction of modern measuring complexes of the coordinate-time support system of Ukraine is impossible without improving mathematical models of quantum standards of frequency (QSF) used in group standards. This work is devoted to the analysis of methods for the stable solution of direct and inverse problems (methods for solving ill-posed problems) in models of the interaction of passive QSF in the process of their comparisons. The priority task is to use these methods for the numerical solution of problems in the design of group QSF and parallel quantum generators of random numbers. Methods for solving such problems are in demand, since they make it possible to create mathematical models of group QSF interaction. These models will enable the design of efficient parallel quantum random number generation devices for high-tech areas of cybersecurity. Varieties of methods such as the method of least squares or the method of the Moore-Penrose pseudo-inverse matrix are used, as a rule when evaluating the metrological parameters of QSF.Robust methods of regularization or filtering, for example, the Kalman or Wiener filter method, are used in the algorithms of group standards, due to the instability of the solution.However, these methods do not work in the presence of an error from the interaction of QSF in the process of their functioning in a group standard or in comparisons. The aim of this work is to analyze and substantiate the formulation of the problem of assessing the potential accuracy characteristics of passive QSF in the presence of an error from the interaction. Regularization parameters when determining the state vector of the group standard are found using signals transmitted by global navigation satellite systems such as GPS\GLONASS in the local differential correction mode.

DOI
10.30837/rt.2021.3.206.03

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Construction of modern measuring complexes of the coordinate-time support system of Ukraine is impossible without improving mathematical models of quantum standards of frequency (QSF) used in group standards. This work is devoted to the analysis of methods for the stable solution of direct and inverse problems (methods for solving ill-posed problems) in models of the interaction of passive QSF in the process of their comparisons. The priority task is to use these methods for the numerical solution of problems in the design of group QSF and parallel quantum generators of random numbers. Methods for solving such problems are in demand, since they make it possible to create mathematical models of group QSF interaction. These models will enable the design of efficient parallel quantum random number generation devices for high-tech areas of cybersecurity. Varieties of methods such as the method of least squares or the method of the Moore-Penrose pseudo-inverse matrix are used, as a rule when evaluating the metrological parameters of QSF.Robust methods of regularization or filtering, for example, the Kalman or Wiener filter method, are used in the algorithms of group standards, due to the instability of the solution.However, these methods do not work in the presence of an error from the interaction of QSF in the process of their functioning in a group standard or in comparisons. The aim of this work is to analyze and substantiate the formulation of the problem of assessing the potential accuracy characteristics of passive QSF in the presence of an error from the interaction. Regularization parameters when determining the state vector of the group standard are found using signals transmitted by global navigation satellite systems such as GPS\GLONASS in the local differential correction mode.
The object of research is the process of mutual synchronization of quantum random number generators (QRNG) in the group standard of quantum noise. A method for generating random numbers is proposed, which relates to the methods of group standardization of the QRNG, and is used to increase the speed and reliability of the random number formation The paper substantiates the mathematical model of quantum phase noise of the QRNG group, which are in a mutual synchronization mode. The method is based on solving the problem of identifying parameters of a group of the same type to the QRNG in the mutual synchronization mode. The solution to this problem requires the availability of reliable and operational data when calculating the Kalman filter parameters necessary for estimating the synchronization parameters of quantum measures of phase noise. The results of experimental studies presented in the article are an example of building a QRNG with a given level of reliability and speed. A feature of the proposed QRNG quantum phase noise measurement system is the synchronization of processing time using GPS signals (Ll C/A).
The necessity of improving the characteristics of metrological for quantum standard of frequency when determining the coordinates of an object on the Earth’s surface or long-term broadcast of large quantity of data in satellite communication systems justified. A new algorism for digital processing of optical signals in the frequency standard is proposed to obtain information about the accuracy signal with making the method of median filtering. The results a research of experimental a characteristics of metrological for quantum standard of frequency based to rubidium - 87 atoms are presented. It is found that improving the long-term frequency stability by 5% using the new algorithm lower the number of bit errors for a long broadcasting information by at least 3%. Also, the error of determining the coordinates of the object is increased by at least 15%.
Krylov subspace methods are among the most extensively studied early fault-tolerant quantum algorithms for estimating ground-state energies of quantum systems. However, the rapid onset of ill-conditioning might make accurate energies difficult or even impossible to retrieve. In this communication, we analyse the numerical stability and statistical problems of these methods using numerical simulations both in the presence and absence of sampling noise. While in ideal numerical simulations the generalized eigenvalue problem indeed becomes unstable with increased Krylov subspace size, we find that, in realistic noisy settings, these methods do not primarily suffer from ill-conditioning. Instead, statistical fluctuations dominate and can prevent reliable solution extraction unless appropriate regularization or filtering techniques are employed. We consequently introduce two new metrics, the imaginary and unitary filters, that successfully assess the reliability of the obtained solutions without any knowledge of the true eigenspectrum.
Recently, there has been a rapid increase in interest in quantum computers. Their work isbased on the use of quantum-mechanical phenomena such as superposition and entanglement forcomputing input data into output data that can actually provide effective performance 3 to 4 orders ofmagnitude higher than any modern computing devices, which will solve the above and others tasks ina natural and accelerated time scale. This article is devoted to solving the problem of research anddevelopment of corrective codes for correcting several types of quantum errors that appear duringcomputational processes in quantum algorithms and models of quantum computing devices. The aimof the work is to study existing methods for correcting various types and types of quantum errors andto create a 3-qubit corrective code for quantum error correction. The work touches upon the tasks ofresearch and development of the functioning methods of quantum circuits and models of quantumcomputing devices. The relevance of these studies lies in the mathematical and software modelingand implementation of corrective codes for correcting several types of quantum errors as part of thedevelopment 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 thequantum computing process. The scientific novelty of this area is primarily expressed in the constantupdating 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 correctingphase types of errors, which allows one to evaluate the own phase of a unitary gate that hasgained access to the quantum state in proportion to its own vector.
The main problems arising during the operation of satellite information systems during the transmission of large amounts of information are considered. It is noted how the disadvantages of the current design of the quantum frequency standard based on rubidium-87 atoms influence the operation of the information transmission system. It is noted that the greatest instabilities during long-term operation of the quantum frequency standard are introduced by processes associated with light shifts in the optical part. Frequency stability decreases, synchronization of time scales of various communication satellites deteriorates. This leads to an increase in the number of errors in the transmission of information. A solution is proposed to improve the metrological characteristics of the rubidium frequency standard. The results of experimental studies of the operation of a satellite information transmission system are presented.
The problem of developing control algorithms in quantum frequency standards based on the effect of coherent population trapping is considered. The development of such algorithms will make it possible to create frequency standards with metrological characteristics that are not inferior to the characteristics of rubidium frequency standards, with reduced power consumption and overall dimensions. A method for studying the dependence of the actual value and frequency instability of quantum frequency standards based on the effect of coherent population trapping on the operating modes of individual parts of the standards is presented. As a criterion for optimizing the laser injection current, the output power of the microwave generator, and the cell temperature, we chose to minimize the effect on the shift of the actual frequency of the standard. A comparative analysis of methods for changing the radiation intensity of a surface-emitting laser with a vertical resonator has been carried out and control algorithms have been developed that take into account the features of these methods. Based on these algorithms, software and tuning methods have been developed in quantum frequency standards based on the effect of coherent population trapping. For the prototype standard, the results of measuring the frequency instability are shown. It is shown that control algorithms and tuning methods can qualitatively change the metrological characteristics of quantum frequency standards based on the effect of coherent population trapping.