T-count optimization of approximate quantum Fourier transform

Byeongyong Park, Doyeol Ahn · 2022 · arXiv 预印本

| 编号 QQFT003 | 主题 量子傅里叶变换 | 链接 arXiv:2203.07739 |

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 quantum Fourier transform (QFT) is a ubiquitous quantum operation that is used in numerous quantum computing applications. The major obstacle to constructing a QFT circuit is that numerous elementary gates are required. Among the elementary gates, T gates dominate the cost of fault-tolerant implementation. Currently, the smallest-known T-count required to construct an n-qubit QFT circuit approximated to error $O(\epsilon )$ is $\sim 8n{\log }_2(n/\epsilon )$. Moreover, the depth of T gates (T-depth) in the approximate QFT circuit is $\sim 2n{\log }_2(n/\epsilon )$. This approximate QFT circuit was constructed using Toffoli gates and quantum adders. In this study, we present a new n-qubit QFT circuit approximated to error $O(\epsilon )$. Our approximate QFT circuit shows a T-count of $\sim 4n{\log }_2(n/\epsilon )$ and a T-depth of $\sim n{\log }_2(n/\epsilon )$. Toffoli gates, which account for half of the T-count in the approximate QFT circuit reported in the previous study, are unnecessary in our construction. Quantum adders, which dominate the leading order term of T-depth in our approximate QFT circuit, are arranged in parallel to reduce T-depth.

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