Petro Kravets

This paper presents a hybrid quantum logistic regression model for binary data classification that combines classical logistic regression methods with quantum computing to improve efficiency and speed up the learning process. Quantum computing is used to represent and process feature and weight vectors as quantum states and to efficiently compute the dot product underlying the logistic function. The use of normalized amplitude coding allows for compact representation of feature vectors and weights, reducing the number of qubits required and potentially speeding up computations for high-dimensional classification problems where classical methods may encounter scalability limitations. The quantum dot product computation is performed using the Hadamard test, which provides a statistical estimate of the probability of measuring an auxiliary qubit. The auxiliary qubit is first put into a superposition state, and after performing controlled unitary operations, amplitude interference is formed, which depends on the scalar product of the feature vector and weight coefficients. The obtained measurement probability is used to estimate the scalar product of the feature vectors and weights. The classical part of the model provides for the execution of operations that are difficult to implement on modern quantum devices, in particular, vector normalization, application of the sigmoid function to estimate the probability of an object belonging to a certain class, calculation of the loss function and iterative update of weight coefficients by the gradient descent method. The purpose of classification is to predict the binary class for an unknown sample based on the training sample. To demonstrate the model, a numerical example is given with a step-by-step calculation of one iteration of logistic regression training. In addition, computer modeling of the hybrid algorithm training process was performed, taking into account the influence of noise on the results of quantum state measurements. A quantum noise model was developed based on the probability of confidence in the measurement result, which is interpreted as an assessment of its reliability in a Bernoulli experiment. Comparison of the obtained results with the classical approach confirms the practical suitability of the hybrid algorithm for binary classification problems. The hybrid model preserves the key properties of classical logistic regression – parameter interpretability and optimization stability, while allowing for the use of quantum advantages for compact data encoding and scalar product computation. This makes the study of hybrid logistic regression relevant for the development of machine learning algorithms on modern quantum platforms.

A stochastic model and an adaptive method for estimating the dominant states of a quantum system have been developed. The proposed approach demonstrates a stable advantage over the frequency-based method under the influence of noise and fluctuations in the measurement process. The dominant state is defined as the most probable basis state into which the wave function of the quantum system collapses after the act of measurement. Determining the dominant state is essential for improving the accuracy of quantum measurements and quantum state reconstruction. The measurement process is modeled on an ensemble of identical quantum systems prepared in the same superposition of basis states. This approach allows the continuation of a series of measurements after the collapse of individual ensemble elements, enabling the accumulation of statistical data and the formation of a reliable estimate of the observation probabilities for each state. The obtained data are used for adaptive updating of the algorithm’s parameters and for constructing a more accurate estimate of the system’s dominant state. The adaptive method is based on a Markovian mechanism of stochastic amplification of the probability of correctly predicting the outcome of measurements of discrete quantum states. The deviation between the predicted and actual results is treated as a penalty function, which is used for dynamic adjustment of the prior probabilities. This approach enables gradual refinement of the dominant state prediction through iterative learning. Based on the proposed method, an adaptive algorithm for predicting the dominant state of a quantum system has been developed and implemented as a computational procedure. The operating principle of the algorithm lies in the multi-stage updating of prediction probabilities for the dominant state, depending on the current value of the penalty function, with the goal of minimizing the expected loss. The convergence of the adaptive process to the actual dominant state of the system has been confirmed by computer simulations. Studies were conducted on the influence of algorithm parameters and quantum system characteristics on accuracy and convergence speed. It was found that the average convergence rate of the adaptive method depends on the intensity of noise affecting the measurement channel, the probabilistic gap between the quantum states, and the learning step parameters. Increasing the variance of white noise or decreasing the probabilistic gap between states leads to slower algorithm convergence, which is consistent with analytical estimates from stochastic optimization theory. The obtained results make it possible to define the necessary constraints on learning parameters to ensure stable convergence under uncertainty. Practical recommendations have been formulated for applying the developed method to problems of quantum computing and quantum information processing.

The aim of the research is the mathematical analysis of quantum superdense coding based on quantum entanglement to increase the efficiency and reliability of information transmission in quantum communication systems. The essence of quantum superdense coding is the ability to transmit two classical bits of information using one qubit, which is part of an entangled pair. The fundamental principles of the superdense quantum coding method are considered. The relevance of the research in the context of the development of secure quantum communications and optimization of information transmission in quantum networks is substantiated. A review of modern scientific publications devoted to the theoretical principles of superdense coding is conducted, which indicate the development potential and practical prospects of this direction of quantum informatics. The analysis of mathematical modeling of quantum superdense encoding and decoding is performed using two alternative approaches – projective measurement in the Bell basis and the inverse Bell transform. It is shown that both approaches allow for the complete recovery of classical information transmitted using entangled quantum states. The advantage of the inverse Bell transform is the simplicity of implementation on quantum devices, the flexibility and accuracy of information processing, and the possibility of scaling, which makes it a reasonable choice in many practical applications. The influence of noise and decoherence on the efficiency of superdense coding has been studied, which is a critical factor in the practical implementation of this method in real quantum systems. A mathematical model of data transmission through a quantum channel under the action of additive white noise has been constructed. An analytical dependence of the probability of correct information recovery on the noise level has been established, which allows us to estimate the limits of reliability of superdense coding in noisy environments. Based on the research, the prospects for the practical application of superdense coding in quantum communication networks, in particular the quantum Internet, as well as in quantum computing and information security systems, have been outlined. The results obtained contribute to the further development of quantum technologies and can be used to create new protocols for highly efficient quantum data transmission.

This article analyzes mathematical models of quantum parallelism based on the transfer of a quantum system into a superposition state. The principles of quantum parallelism and its mathematical foundations are substantiated. To demonstrate the quantum advantage, mathematical models of fundamental quantum algorithms Deutsch-Joža and Grover are analyzed, which illustrate the efficiency of quantum computing compared to classical methods. The Deutsch-Joshy algorithm is considered, which generalizes the problem of determining the type of a binary function by extending it to a set of arguments written in a quantum register. This algorithm allows determining whether a function is constant or balanced in a single quantum call, while in classical calculations this requires exponential time. It is noted that although the Deutsch-Joshy algorithm demonstrates the possibilities of parallel quantum computing, it is of mainly theoretical importance. Grover’s algorithm implements quantum parallel computing for the practical problem of searching for an element in an unordered database. It is based on iterative amplification of the amplitude of the state corresponding to the searched element and provides quadratic speedup compared to classical algorithms. In addition to database search, Grover’s algorithm can be adapted to solve other optimization problems. The work of the considered algorithms is illustrated by numerical examples, which simplifies the understanding of their principles and contributes to the further methodological development of parallel quantum computing. The article also outlines the advantages of quantum parallelism over classical computing and identifies the prospects for the application of parallel quantum algorithms.

This article discusses the practical aspects of applying logistic regression for binary data classification. Logistic regression determines the probability of an object belonging to one of two classes. This probability is calculated with the help of a sigmoid function, the argument of which is a linear convolution of the feature vector of the object with the weighting coefficients obtained during the minimization of the logarithmic loss function. Predicted class labels are determined by comparing the calculated probability with a given threshold value. The logistic regression study was performed using the computer simulation method. For this, a software complex was developed, the work of which reproduces the main stages of logistic regression: preparation of input data, training, testing with determination of quality metrics of binary classification, application of the logistic regression method for data classification in practice. The paper examines the effect of overlapping and imbalance of classes in the input data set on the efficiency of binary classification. The overlapping of classes is modeled by the formation of input data based on two shifted relative to each other density functions of the normal distribution of random variables. Class imbalance is simulated by the probability of switching between these features. It is shown that when the distance between the mathematical expectations of the density functions of the normal distribution decreases or when the dispersion of random variables increases, the overlapping of relevant classes increases, which leads to an increase in the number of objects that the classifier can assign to one or another class. Approaching the probability of switching between the distribution functions of random variables to the extreme values of the unit interval leads to an increase in class imbalance, which is manifested in an increase in the number of elements of the input data set labeled with the label of the same class. It has been experimentally confirmed that the AUC ROC metric, popular in binary classification problems, is dependent on the degree of class overlap and relatively resistant to class imbalance.

This article reviews the theoretical aspects of logistic regression for binary data classification, including data preparation processes, training, testing, and model evaluation metrics. Requirements for input data sets are formulated, methods of coding categorical data are described, methods of scaling input features are defined and substantiated. A scheme for learning logistic regression using the gradient descent method has been developed to minimize the loss function by the appropriate adjustment of the weights of the features of the sample of objects intended for classification. Features of the construction of recurrent methods of classical and stochastic gradient descent are determined. The requirements for the organization of the data sample for the multi-stage learning model in order to avoid overtraining or undertraining of logistic regression are described. The scheme of testing the trained logistic regression is given and the main quality metrics of binary classification are described. The influence of the height of the classification threshold on the efficiency of logistic regression was noted. According to the results of the work, the directions of perspective research of logistic regression are outlined.

In this article, the mathematical justification of logistic regression as an effective and simple to implement method of machine learning is performed. A review of literary sources was conducted in the direction of statistical processing, analysis and classification of data using the logistic regression method, which confirmed the popularity of this method in various subject areas. The logistic regression method was compared with the linear and probit regression methods regarding the possibility of predicting the probabilities of events. In this context, the disadvantages of linear regression and the advantages and affinity of logit and probit regression methods are noted. It is indicated that the possibility of forecasting probabilities and binary classification by the method of logistic regression is provided by the use of a sigmoid function with the property of compressive transformation of an argument with an unlimited numerical value into a limited range from 0 to 1 real value of the function. The derivation of the sigmoid function in two different ways is described: based on the model of the logarithm of the odds of events and the model of logistic population growth. Based on the method of maximum likelihood, the construction of a logarithmic loss function was demonstrated, the use of which made it possible to move from a multi-extremal nonlinear regression problem to a unimodal optimization problem. Methods of regularization of the loss function are presented to control the complexity and prevent retraining of the logistic regression model.

Accounting of premises is the process of storing, processing and manipulating accounting data of premises. In IT companies, effective premises accounting is of particular importance: it can help reduce costs, improve staff performance, and increase business efficiency. The need to keep records of the premises of an IT company always arises in the case of many offices or many manipulations of their data. Optimal use of space is one of the key factors in ensuring the efficiency of IT companies. The convenience of operational access to all the relevant information on the premises already greatly simplifies the conduct of business for IT companies. The availability of information technology with an analysis and decision- making system reduces the complexity of some accounting processes to a few mouse clicks by one of the relevant managers of the company. Study object – is the process of accounting for premises in an IT company, including the processes of collecting, processing, analysing, and displaying information necessary for efficient use of space. Scope of research - is the information technology for maintaining records of the IT company facilities, which allows to use of the space as efficiently as possible while minimizing costs. The goal this of research is to develop an IT company’s premises accounting information technology that will serve not only as a place to store and review accounting data but also as a platform for reserving places or premises and analysing their condition in accordance with regulatory documents and laws of Ukraine. The development of information technology for the accounting of premises for IT companies is a key component for solving the problem of efficient use of space and reducing costs. The developed technology allows collecting, processing, and analysing information on the use of premises in real-time, which will ensure effective control over the use of space and allow timely response to changes in requirements. This technology should be considered as a decision-making system, which not only manipulates data but also helps analyse and select information according to the user’s relevant requests. Among the important features and functions of the premise accounting technology can be attributed: to the creation, editing and deletion of premises from the system; analysis of the condition of the premises; access to all accounting and analytical data using a chatbot, which is built using an artificial intelligence system; booking a place or room for any amount of time during the day; review of current reservations of each room: review of all created reservations of a specific user; manipulation of employee data: registration, editing and deletion of users from the system, which can only be done by the manager.

This paper describes an information system for monitoring and analyzing reviews on social networks to form recommendations for the purchase of goods. This system is designed to be used by customers to speed up and facilitate the search for the necessary products on e-commerce resources. Successful selection of a quality product according to the desired criteria is extremely important, as it saves search time and customer money. Analyzing comments on the network, the information system recommends the product if there is a preponderance of positive feedback on it. The purpose of the work, object and subject of research, scientific novelty and practical significance of the work are formulated. An analysis of the peculiarities of the studied subject area and known means of solving the problem was carried out. Systems used in online marketing were used as a prototype system for generating recommendations based on feedback analysis. Comparative characteristics of the system with analogues were conducted and it was determined that the system is unique, and its development is relevant, since known existing similar systems do not recommend products to users based on the feedback of other users. The general goal of system development is determined, the purpose, place of application of the system, development and implementation of the system are described. The criteria that are put forward when defining the goals are defined. Using the method of analysis of hierarchies, it was determined that the type of product being developed is a decision support system. A conceptual model of the system has been developed. Project requirements are modeled – business requirements, user requirements, functional requirements, non-functional requirements. Input and output data of the system are defined. The decision-making system is based on an algorithm for sentiment analysis of social networks users using the logistic regression method. Logistic regression is one of the most common machine learning algorithms that is easy to implement for classifying sets of linearly separable clusters of data. It quickly learns on large data sets and guarantees reliable results. Economic, functional, financial and time effects should be expected from the implementation of such a recommendation system.

This paper describes the requirements for the project of an information sales system on the platform of charitable online auctions, which offers a fundamentally new way to sell valuable property, such as real estate or transport. The designed information system is a non-standard solution for the implementation of auction sales, since in economically unstable times it is intended to become an alternative way for sellers to expose their property as a lot; to play a lot between the participants of the auction and give a chance to low-income segments of the population to become owners of valuable property for a relatively small amount of the bid in the auction; pay part of the collected amount in favor of charitable foundations for which users will vote when participating in the auction; enrich the state budget by paying taxes on the purchase and sale procedure. The expediency of creating such an information system was assessed on the basis of comparing it with the existing prototypes. To substantiate the relevance of the project, a system of experimental evaluation of the characteristics of the designed system and its analogues has been developed according to a number of criteria. A number of advantages and critical differences of the system project have been identified. On the basis of the project management method S.M.A.R.T. the goals of creating an information system are formulated and a list of tasks to achieve them is determined. Structural, functional, informational, business and client requirements for the project are outlined. The main means of developing an IT project in TypeScript on the Node.js and Angular platforms are indicated. Integration of the information system with the Fondy payment system to save proceeds from the auction is proposed. The risks of project implementation are identified and ways to minimize their impact are outlined.