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