RESEARCH AND DEVELOPMENT OF DEPTH OPTIMIZED CIRCUITS IN QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM
S. M. Gushanskiy, Viktor Potapov, V.I. Bozhich · Известия Южного федерального университета. Технические науки · 2023
One of the main challenges faced by researchers in the field of quantum computing is the problemof 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 quantumalgorithms with a focus on depth, is updated. The depth of quantum circuits is one of the critical parametersin 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 practicalresults for quantum computing in the context of optimization problems. This study analyzes the use ofa quantum approximate optimization algorithm for solving complex combinatorial optimizationproblems. However, in the process of using this algorithm we encounter a serious limitation – noisein the quantum system, which significantly reduces its efficiency. To overcome the influence of noiseand improve the efficiency of quantum algorithms, several methods have been proposed. This paperpresents a greedy heuristic algorithm aimed at reducing the impact of noise. The main goal of thisalgorithm is to find a spanning tree of minimum height. This, in turn, reduces the overall depth ofquantum circuits and minimizes the number of CNOT gates, which is key to optimizing quantumcomputing. Through numerical analysis, it was demonstrated that the proposed greedy heuristicalgorithm is capable of significantly increasing the probability of successful completion of each iterationin the problem of finding the maximum cut in a graph by 10 times. Moreover, the study confirmsthat the average depth of the quantum circuit generated by the proposed heuristic algorithm is stilllinearly dependent on the size of the input data, but the slope of this linear dependence is reducedfrom 1 to 0.11 by using the proposed method.