RESEARCH AND DEVELOPMENT OF DEPTH OPTIMIZED CIRCUITS IN QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM

Abstract

One of the main challenges faced by researchers in the field of quantum computing is the problem of noise in quantum systems. Noise can significantly limit the performance of quantum algorithms. It is in this context that our research, aimed at the development and optimization of quantum algorithms with a focus on depth, is updated. The depth of quantum circuits is one of the critical parameters in the development of quantum algorithms. Optimized circuits with improved depth have the potential to significantly reduce the impact of noise, which in turn should lead to improved efficiency. We aim to provide solutions that not only address technical constraints, but also provide practical results for quantum computing in the context of optimization problems. This study analyzes the use of a quantum approximate optimization algorithm for solving complex combinatorial optimization problems. However, in the process of using this algorithm we encounter a serious limitation – noise in the quantum system, which significantly reduces its efficiency. To overcome the influence of noise and improve the efficiency of quantum algorithms, several methods have been proposed. This paper presents a greedy heuristic algorithm aimed at reducing the impact of noise. The main goal of this algorithm is to find a spanning tree of minimum height. This, in turn, reduces the overall depth of quantum circuits and minimizes the number of CNOT gates, which is key to optimizing quantum computing. Through numerical analysis, it was demonstrated that the proposed greedy heuristic algorithm is capable of significantly increasing the probability of successful completion of each iteration in the problem of finding the maximum cut in a graph by 10 times. Moreover, the study confirms that the average depth of the quantum circuit generated by the proposed heuristic algorithm is still linearly dependent on the size of the input data, but the slope of this linear dependence is reduced from 1 to 0.11 by using the proposed method.