Approximate Quantum Fourier Transform in Logarithmic Depth on a Line

Elisa Bäumer, David Sutter, Stefan Woerner · 2025 · arXiv 预印本

| 编号 QQFT006 | 主题 量子傅里叶变换 | 链接 arXiv:2504.20832 |

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 approximate quantum Fourier transform (AQFT) on $n$ qubits can be implemented in logarithmic depth using $8n$ qubits with all-to-all connectivity, as shown in [Hales, PhD Thesis Berkeley, 2002]. However, realizing the required all-to-all connectivity can be challenging in practice. In this work, we use dynamic circuits, i.e., mid-circuit measurements and feed-forward operations, to implement the AQFT in logarithmic depth using only $4n$ qubits arranged on a line with nearest-neighbor connectivity. Furthermore, for states with a specific structure, the number of qubits can be further reduced to $2n$ while keeping the logarithmic depth and line connectivity. As part of our construction, we introduce a new implementation of an adder with logarithmic depth on a line, which allows us to improve the AQFT construction of Hales.

读法提示

该摘要中的全部收益都落在比特数与连接性上（$8n$ 全连接 → $4n$ 最近邻 → 特定结构 $2n$），深度维持对数不变。它没有主张降低 T 数。本站合成与成本一词条据此把它归入”重排 / 省资源而非省 T 数”一类。

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