论文标题
多尺度传输方程的量子差异方法的时间复杂性分析
Time complexity analysis of quantum difference methods for the multiscale transport equations
论文作者
论文摘要
我们研究了使用量子算法解决多尺度传输方程的有限差异方法的时间复杂性。我们发现，标准明确方案量表的经典治疗和量子处理的时间复杂性为$ \ MATHCAL {O}（1/\ VAREPSILON）$，其中$ \ varepsilon $是较小的扩展参数，而基于基于AP）的（ap）方案的复杂性consection $ \ vareps $ \ $ \ $ \。这表明在求解多尺度运输或动力学方程时，使用AP（以及可能其他有效的多尺度）方案来解决量子计算中的多尺度问题仍然非常重要。
We investigate time complexities of finite difference methods for solving the multiscale transport equation with quantum algorithms. We find that the time complexities of both the classical treatment and quantum treatment for a standard explicit scheme scale as $\mathcal{O}(1/\varepsilon)$, where $\varepsilon$ is the small scaling parameter, while the complexities for the even-odd parity based Asymptotic-Preserving (AP) scheme do not depend on $\varepsilon$. This indicates that it is still of great importance to use AP (and probably other efficient multiscale) schemes for multiscale problems in quantum computing when solving multiscale transport or kinetic equations.
