发表机构
New York University（纽约大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对结构化量子信号，提出一种利用非线性振幅变换搜索全局极值的算法，实现多对数查询复杂度，并在大规模湍流数据中验证了其高效性和量子优势。
AI 中文摘要
物理系统的极值在定义上就是罕见的，然而它们却可能主导系统某些最具后果性和异常性的行为。它们的稀疏性使得在大数据集中识别它们变得尤为昂贵。量子计算提供了一种潜在的方式来降低这一成本。挑战在于，量子振幅不能简单地通过传统的搜索预言机进行读取、复制、比较或标记。在此，我们引入一种算法，用于搜索振幅编码的量子信号，该算法利用了信号的内在结构。通过非线性振幅变换，该算法能够识别并认证全局极值，同时对于结构化信号，将有效搜索空间指数级地缩减。我们建立了在数据规模$N$上的多对数查询复杂度，同时保证了全局完备性、高效的经典验证，以及一个用于量化可利用结构的可测量标准。我们使用计算湍流数据来演示该框架。应用于来自一个包含超过十亿网格点的$1024^3$模拟的速度梯度线切割，该算法持续地隔离出极端尾部，并将中位搜索空间缩减至$O(\log N)$。湍流特有的簇状结构进一步加速了搜索。这些结果建立了物理结构与极值搜索中量子优势之间的直接联系。为便于阅读，正文强调了核心思想和结果，而理论推导则提供在附录中。
英文摘要
Extreme values of a physical system are rare by definition, yet they can govern some of its most consequential and anomalous behavior. Their sparsity makes them particularly costly to identify in large data sets. Quantum computation offers a potential way to reduce this cost. The challenge is that quantum amplitudes cannot simply be read, copied, compared, or marked using conventional search oracles. Here we introduce an algorithm for searching amplitude-encoded quantum signals that exploits their underlying structure. Through a nonlinear amplitude transformation, the algorithm identifies and certifies a global extremum while exponentially reducing the effective search space for structured signals. We establish a polylogarithmic query complexity in the data size $N$, together with global completeness, efficient classical verification, and a measurable criterion for quantifying exploitable structure. We demonstrate the framework using computational turbulence data. Applied to line cuts of velocity gradients from a $1024^3$ simulation containing more than one billion grid points, the algorithm consistently isolates the extreme tail and reduces the median search space to $O(\log N)$. The clustered structure characteristic of turbulence further accelerates the search. These results establish a direct connection between physical structure and quantum advantage in extreme-value search. For accessibility, the main text emphasizes the central ideas and results, while the theoretical derivations are provided in the Appendices.
Comments33 pages, 5 figures, 2 tables
