布尔矩阵乘法的一种时间有效的输出敏感量子算法
A Time-Efficient Output-Sensitive Quantum Algorithm for Boolean Matrix Multiplication
摘要：
本文提出了一种在$\tilde O(n\sqrt{\ell}+\ell\sqrt{n})$时间内计算两个$n\times n$布尔矩阵乘积的量子算法，其中$\ell$是乘积中非零元素的个数.这改进了Buhrman和Špalek（SODA'06）和Le Gall（SODA'12）在时间复杂度设置中的布尔矩阵乘法的先前输出敏感量子算法。我们还表明，我们的方法不能进一步改进，除非取得突破：我们证明，任何显着的改进将意味着存在的量子搜索的基础上，乘以两个$n\times n$布尔矩阵在$O(n^{5/2-\varepsilon})$时间，为一些常数$\varepsilon>0$的算法。
英文摘要：
This paper presents a quantum algorithm that computes the product of two $n\times n$ Boolean matrices in $\tilde O(n\sqrt{\ell}+\ell\sqrt{n})$ time, where $\ell$ is the number of non-zero entries in the product. This improves the previous output-sensitive quantum algorithms for Boolean matrix multiplication in the time complexity setting by Buhrman and Špalek (SODA'06) and Le Gall (SODA'12). We also show that our approach cannot be further improved unless a breakthrough is made: we prove that any significant improvement would imply the existence of an algorithm based on quantum search that multiplies two $n\times n$ Boolean matrices in $O(n^{5/2-\varepsilon})$ time, for some constant $\varepsilon>0$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
