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.