DEVELOPMENT AND RESEARCH OF A QUANTUM GRAPH MODEL FOR IMAGE COMPRESSION AND RECONSTRUCTION

Abstract

The article discusses in detail the methods and approaches to the application of quantum algorithms for solving optimization and image processing problems. Particular attention is paid to quantum approximate optimization (QAO) and the use of quantum networks for data compression and reconstruction problems. QAO is a hybrid algorithm that combines quantum and classical computational processes, allowing one to efficiently solve complex combinatorial problems. QAO is based on parameterized unitary operations that are optimized during iterations. This approach makes it possible to consider the unique features of the quantum nature of information, which in some cases allows achieving higher performance than when using exclusively classical methods. In the process of implementing QAO, one of the main obstacles remains the problem of noise, which can arise, for example, when using CNOT gates. The article discusses various strategies for reducing the noise level, which is an important task for ensuring the stability and improving the accuracy of quantum algorithms. For example, methods for isolating individual operations and correcting errors are considered, which allows one to minimize the impact of noise on the calculation results and improve the accuracy of quantum optimization. The authors also propose a graph interpretation of quantum models based on the use of tensor networks. This approach allows for efficient simplification of computational graphs, thereby optimizing the resources required to perform complex quantum operations. This method also demonstrates high efficiency in image compression and restoration tasks, which opens up new prospects for the application of quantum networks in data processing. The article describes the structure of quantum networks, including multilayer quantum gates, which allow for deeper and more detailed image processing, providing both efficient compression and high-quality data restoration. An analysis of various types of quantum gates, such as Hadamard, Pauli-X, Pauli-Y, and T-gates, was also conducted. These gates play a key role in the efficiency of quantum algorithms, since each of them contributes to quantum dynamics and the way quantum states are manipulated