Abstract

In this work, we consider the actual problem of separating the roots of nonlinear systems of equations in the case of many variables. The known method of reducing the problem of solving the system to an equivalent extremal problem, which is supposed to be solved by one of the stochastic optimization methods, is used. As the latter, the modeling method of annealing simulation and its modification, which are especially interesting because they allow effective implementation on quantum computers, are chosen. Since quantum computers based on simulated annealing demonstrate quantum superiority, the obtained results can be useful in solving systems of equations on these computers.

中文翻译：

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非线性方程组的根分离。随机方法

摘要

在这项工作中，我们考虑了在多变量情况下分离非线性方程组根的实际问题。使用将解决系统的问题简化为等效的极值问题的已知方法，该问题应该通过随机优化方法之一来解决。作为后者，选择了退火模拟及其修改的建模方法，这些方法特别有趣，因为它们允许在量子计算机上有效地实现。由于基于模拟退火的量子计算机展示了量子优势，因此所获得的结果可用于在这些计算机上求解方程组。