标题： 超指数级量子优势用于找到球体的中心 显示英文标题

标题： Super-exponential quantum advantage for finding the center of a sphere

摘要： 本文考虑了在有限域上的向量空间中，根据球面上随机点的样本求解球心的几何问题。 我们提出了一种基于连续时间量子行走的量子算法，该算法只需常数量的样本即可找到球心。 我们还通过归约到一个古老而基本的代数结果——Warning定理的第二条，证明了对于同一任务的任何经典算法都需要大约与向量空间维度相同数量的样本。 因此，首次揭示了一个自然且直观的几何问题中的超指数级量子优势。 显示英文摘要

摘要： This article considers the geometric problem of finding the center of a sphere in vector space over finite fields, given samples of random points on the sphere. We propose a quantum algorithm based on continuous-time quantum walks that needs only a constant number of samples to find the center. We also prove that any classical algorithm for the same task requires approximately as many samples as the dimension of the vector space, by a reduction to an old and basic algebraic result -- Warning's second theorem. Thus, a super-exponential quantum advantage is revealed for the first time for a natural and intuitive geometric problem.