Quantum Fast Fourier Transform Viewed as a Special Case of Recursive Application of Cosine-Sine Decomposition

Robert R. Tucci · 2004 · arXiv 预印本

| 编号 QQFT019 | 主题 量子傅里叶变换 | 链接 arXiv:quant-ph/0411097 |

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。

A quantum compiler is a software program for decomposing (“compiling”) an arbitrary unitary matrix into a sequence of elementary operations (SEO). Coppersmith showed that the $n$-bit Discrete Fourier Transform matrix $U_{FT}$ can be decomposed in a very efficient way, as a sequence of order($n^2$) elementary operations. Can a quantum compiler that doesn’t know a priori about Coppersmith’s decomposition nevertheless decompose $U_{FT}$ as a sequence of order($n^2$) elementary operations? In other words, can it rediscover Coppersmith’s decomposition by following a much more general algorithm? Yes it can, if that more general algorithm is the recursive application of the Cosine-Sine Decomposition (CSD).

读法提示

这是一条”从通用分解算法里重新发现 QFT”的结果。它与QFT 的门结构里讲的 $H$ + 受控相位阶梯是同一件事的两种叙述：一条自顶向下手推，一条自底向上分解。

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