Essence and structure of a quantum algorithm for solving systems of linear algebraic equations

In the framework of this work, a quantum algorithm has been implemented that allows one to solve systems of linear algebraic equations of various dimensions. The algorithm reflects the tangible time gain of the solution with the help of quantum-amplitude amplification with variable time. The article analyzes the basic concepts of the temporal complexity of quantum algorithms that can be used to implement them. The relevance of this article is to consider one of the approaches to the construction of new quantumoriented algorithms and the great importance of this topic and research for the implementation of quantum computing devices.