dorsal/arxiv
View SchemaA new algorithm for producing quantum circuits using KAK decompositions
| Authors | Yumi Nakajima, Yasuhito Kawano, Hiroshi Sekigawa |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0509196 |
| URL | https://arxiv.org/abs/quant-ph/0509196 |
Abstract
We provide a new algorithm that translates a unitary matrix into a quantum circuit according to the G=KAK theorem in Lie group theory. With our algorithm, any matrix decomposition corresponding to type-AIII KAK decompositions can be derived according to the given Cartan involution. Our algorithm contains, as its special cases, Cosine-Sine decomposition (CSD) and Khaneja-Glaser decomposition (KGD) in the sense that it derives the same quantum circuits as the ones obtained by them if we select suitable Cartan involutions and square root matrices. The selections of Cartan involutions for computing CSD and KGD will be hown explicitly. As an example, we show explicitly that our method can automatically reproduce the well-known efficient quantum circuit for the n-qubit quantum Fourier transform.
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"date_created": "2026-03-02T18:02:20.479000Z",
"date_modified": "2026-03-02T18:02:20.479000Z",
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"abstract": "We provide a new algorithm that translates a unitary matrix into a quantum\ncircuit according to the G=KAK theorem in Lie group theory. With our algorithm,\nany matrix decomposition corresponding to type-AIII KAK decompositions can be\nderived according to the given Cartan involution. Our algorithm contains, as\nits special cases, Cosine-Sine decomposition (CSD) and Khaneja-Glaser\ndecomposition (KGD) in the sense that it derives the same quantum circuits as\nthe ones obtained by them if we select suitable Cartan involutions and square\nroot matrices. The selections of Cartan involutions for computing CSD and KGD\nwill be hown explicitly. As an example, we show explicitly that our method can\nautomatically reproduce the well-known efficient quantum circuit for the\nn-qubit quantum Fourier transform.",
"arxiv_id": "quant-ph/0509196",
"authors": [
"Yumi Nakajima",
"Yasuhito Kawano",
"Hiroshi Sekigawa"
],
"categories": [
"quant-ph"
],
"title": "A new algorithm for producing quantum circuits using KAK decompositions",
"url": "https://arxiv.org/abs/quant-ph/0509196"
},
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"source": {
"execution_id": "ac8ea483-f13f-4e31-8229-7e8e4094f04e",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
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