具有$O(n \log n)$深度和O（n）Ancillae的GCD计算量子电路
Quantum Circuits for GCD Computation with $O(n \log n)$ Depth and O(n) Ancillae
摘要：
GCD计算和欧几里德算法的变体在经典和量子算法中都有广泛的应用。在本文中，我们提出了量子电路的GCD计算与$O(n \log n)$深度与O（n）的附属。时间复杂度为O（n），因此，时间复杂度为O（n）。所提出的构造基于二进制GCD算法，并且受益于用于1位移位、比较/减法和管理辅助的对数深度电路。与传统电路一样，最坏情况下的门数仍然是$O(n^2)$。
英文摘要：
GCD computations and variants of the Euclidean algorithm enjoy broad uses in both classical and quantum algorithms. In this paper, we propose quantum circuits for GCD computation with $O(n \log n)$ depth with O(n) ancillae. Prior circuit construction needs $O(n^2)$ running time with O(n) ancillae. The proposed construction is based on the binary GCD algorithm and it benefits from log-depth circuits for 1-bit shift, comparison/subtraction, and managing ancillae. The worst-case gate count remains $O(n^2)$, as in traditional circuits.
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。
