AI 中文总结
该研究明确量子计算算法求解交流潮流问题实现量子优势的运行时间复杂度条件，推导了基于门的量子计算算法的运行时间基准表达式，指出其相对经典牛顿-拉夫逊潮流算法的潜在优势领域。
AI 中文摘要
本文旨在明确量子计算（QC）算法在求解交流潮流（ACPF）问题时实现量子优势所需的条件，重点关注运行时间复杂度。首先，我们建立了一个基准，用于衡量量子计算迭代求解器相对于经典牛顿-拉夫逊潮流（NRLF）算法的优势。接下来，我们推导了任何基于门的量子计算算法的端到端运行时间复杂度的基准表达式为Ω(Nκ/ε)，该表达式反映了对系统规模N、条件数κ和误差容限ε的依赖关系。最后，我们强调了量子计算算法在解决标准ACPF问题时可能比NRLF算法具有潜在优势的关键领域。
英文摘要
This paper aims to contextualize the requirements for Quantum Computing (QC) algorithms to achieve a quantum advantage in solving the alternating current power flow (ACPF) problem, with a focus on runtime complexity. First, we establish a benchmark for a QC iterative solver to demonstrate an advantage over the classical Newton-Raphson Load Flow (NRLF) algorithm. Next, we derive a baseline expression for the end-to-end runtime complexity of any Gate-based QC algorithm as $Ω(N κ/\varepsilon),$ reflecting dependence on system size $N$, condition number $κ$, and error tolerance $\varepsilon$. Finally, we highlight key areas where QC algorithms may offer potential benefits over NRLF in addressing the standard ACPF problem.
