Approximate Quantum Fourier Transform with O(n log(n)) T gates

Yunseong Nam, Yuan Su, Dmitri Maslov · 2018（期刊 2020）· npj Quantum Information 6, 26

| 编号 QQFT005 | 主题 量子傅里叶变换 | 链接 arXiv:1803.04933 |

摘要

摘要保留原文（英文）

摘要取自 arXiv / 出版方元数据，未作翻译，以保证与原文一致。

The ability to implement the Quantum Fourier Transform (QFT) efficiently on a quantum computer facilitates the advantages offered by a variety of fundamental quantum algorithms, such as those for integer factoring, computing discrete logarithm over Abelian groups, solving systems of linear equations, and phase estimation, to name a few. The standard fault-tolerant implementation of an $n$-qubit unitary QFT approximates the desired transformation by removing small-angle controlled rotations and synthesizing the remaining ones into Clifford+T gates, incurring the T-count complexity of $O(n{\log }^2(n))$. In this paper, we show how to obtain approximate QFT with the T-count of $O(n\log (n))$. Our approach relies on quantum circuits with measurements and feedforward, and on reusing a special quantum state that induces the phase gradient transformation. We report asymptotic analysis as well as concrete circuits, demonstrating significant advantages in both theory and practice.

读法提示

该摘要同时给出了本站反复引用的两个基线数字：标准容错 QFT 的 $O(n{\log }^{2}n)$ T 数，以及本文的 $O(n\log n)$。前者是”去掉小角度受控旋转 + 把剩余受控旋转合成到 Clifford+T”这两步共同造成的，后者依赖测量与前馈。

本站词条在引用该文献时，会以 wikilink（sources/QQFT005）链接到本页；右侧「反向链接」面板自动列出所有引用它的词条。