ASPECTS OF THE PRACTICAL APPLICATION OF QUANTUM-INSPIRED ALGORITHMS FOR SYSTEMS OF LINEAR EQUATIONS

Maslennikov Vladimir Vladimirovich

The article discusses the features of the practical application of quantum-inspired algorithms in problems of linear algebra. It is determined that these algorithms have an exponential asymptotic acceleration in comparison with the known classical methods for solving problems associated with low-rank matrices. A theoretical analysis of algorithms based on mathematical modeling is carried out, aimed at identifying specific features in their practical implementation in order to determine the characteristics and properties in which quantum-inspired algorithms can outperform existing classical approaches. The study shows that practically quantum-inspired algorithms can achieve a positive effect if a number of conditions are strictly observed: low rank of the input matrix, low condition number, and significantly high dimension of the input matrix.

Keywords:quantum-inspired algorithms, linear algebra, approximation, singular value decomposition, Monte Carlo method, complexity estimation of algorithms.