dorsal/arxiv
View SchemaQuantum Fast Fourier Transform Viewed as a Special Case of Recursive Application of Cosine-Sine Decomposition
| Authors | Robert R. Tucci |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0411097 |
| URL | https://arxiv.org/abs/quant-ph/0411097 |
Abstract
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 $\nb$-bit Discrete Fourier Transform matrix $U_{FT}$ can be decomposed in a very efficient way, as a sequence of order($\nb^2$) 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($\nb^2$) 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).
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"abstract": "A quantum compiler is a software program for decomposing (\"compiling\") an\narbitrary unitary matrix into a sequence of elementary operations (SEO).\nCoppersmith showed that the $\\nb$-bit Discrete Fourier Transform matrix\n$U_{FT}$ can be decomposed in a very efficient way, as a sequence of\norder($\\nb^2$) elementary operations. Can a quantum compiler that doesn\u0027t know\na priori about Coppersmith\u0027s decomposition nevertheless decompose $U_{FT}$ as a\nsequence of order($\\nb^2$) elementary operations? In other words, can it\nrediscover Coppersmith\u0027s decomposition by following a much more general\nalgorithm? Yes it can, if that more general algorithm is the recursive\napplication of the Cosine-Sine Decomposition (CSD).",
"arxiv_id": "quant-ph/0411097",
"authors": [
"Robert R. Tucci"
],
"categories": [
"quant-ph"
],
"title": "Quantum Fast Fourier Transform Viewed as a Special Case of Recursive Application of Cosine-Sine Decomposition",
"url": "https://arxiv.org/abs/quant-ph/0411097"
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