构造功能性量子算法
Engineering Functional Quantum Algorithms
AI总结：
本文证明当幺正矩阵U满足U^m为标量矩阵时，其函数可用至多O(mK+m^2log m)个基本门的通用量子电路实现，并由此得到分数傅里叶变换的高效电路。
摘要：
假设已知幺正矩阵U的含K个基本门的量子电路，且对某正整数m，U^m为标量矩阵。我们证明U的函数可在量子计算机上以至多O(mK+m^2log m)个基本门实现。该函数由结构极简的通用量子电路实现。此外，我们还得到了分数傅里叶变换的高效电路。
英文摘要：
Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most O(mK+m^2log m) elementary gates. The functions of U are realized by a generic quantum circuit, which has a particularly simple structure. Among other results, we obtain efficient circuits for the fractional Fourier transform.
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。
