发表机构
University of Wisconsin-Madison; IT University of Copenhagen（威斯康星大学麦迪逊分校; 哥本哈根科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究为Shor量子因式分解与离散对数算法确定了尖锐且趋于零的噪声阈值，低于阈值算法在期望多项式时间内成功，高于阈值则对正密度素数集合可证明失败。
AI 中文摘要
我们研究了当噪声影响量子傅里叶变换中的精确受控旋转门时，Shor量子因式分解和离散对数算法的渐近行为。改进Cai（2024）及Cai和Young（2025）的结果，我们确定了一个尖锐且趋于零的噪声阈值。若噪声水平低于此阈值，则两种算法在期望多项式时间内成功。若噪声水平超过此阈值，则当底层素数属于正密度集合时，算法在期望多项式时间内可证明地无法解决各自的问题。
英文摘要
We study the asymptotic behavior of Shor's quantum factoring and discrete log algorithms when noise affects the precise controlled rotation gates in their quantum Fourier transforms. Improving the results of Cai (2024) and Cai and Young (2025), we identify a sharp and vanishingly small noise threshold. If the noise level lies below this threshold, then the two algorithms succeed in expected polynomial time. If the noise level exceeds this threshold, then the algorithms provably fail to solve their respective problems in expected polynomial time when the underlying primes belong to a set of positive density.
Comments21 pages
