AI 中文总结
研究量子计算机在潮流计算中的局限性，通过分析实际电网特性，证明其限制了直流潮流计算的量子优势，且在交流潮流、最优潮流和机组组合中也存在障碍，所有证明经Lean 4源代码形式验证。
AI 中文摘要
本文证明了实际电网特性限制了量子计算机在潮流计算中的适用性。在输电网络中常见的分为两个仅通过少数母线相连的大区域的电网，会使直流电纳矩阵的伪条件数随网络规模呈多项式增长，而连接此类区域的长线路链会使其呈二次增长，这使近期的经验观察更加严谨。这些界限对于任意有界随机线路电纳也极大概率成立。结合查询和层析成像下限，这排除了在每个读出水平上直流潮流的端到端量子优势，且这些障碍在交流潮流、最优潮流和机组组合中依然存在。所有证明都通过Lean 4源代码进行了形式验证。
英文摘要
This letter proves realistic grid properties limit the applicability of quantum computers for power flow. Grids that split into two large regions meeting at only a few buses, common in transmission networks, force the pseudo condition number of the DC susceptance matrix to grow polynomially in the network size, and long chains of lines bridging such regions force quadratic growth. This rigorously verifies the empirical results of recent work. We also show that the theory holds without model information with high probability for independent bounded random line susceptances. Combined with query and tomography lower bounds, this precludes end-to-end quantum advantage for DC power flow at every readout level, and these obstructions persist through AC power flow, optimal power flow, and unit commitment. All proofs are formally verified in Lean 4.
