dorsal/arxiv
View SchemaA constructive algorithm for the Cartan decomposition of SU(2^N)
| Authors | Henrique N. Sá Earp, Jiannis K. Pachos |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0505128 |
| URL | https://arxiv.org/abs/quant-ph/0505128 |
| DOI | 10.1063/1.2008210 |
| Journal | Jour. Math. Phys. 46, 1 (2005) |
Abstract
We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser decomposition of a general element G of SU(2^N) in terms of its `Cartan' and `non-Cartan' components. This effectively factors G in terms of group elements that belong in SU(2^n) with n<N, a procedure that can be iterated down to n=2. We show that every step reduces to solving the zeros of a matrix polynomial, obtained by truncation of the Baker-Campbell-Hausdorff formula, numerically. All computational tasks involved are straightforward and the overall truncation errors are well under control.
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"abstract": "We present an explicit numerical method to obtain the Cartan-Khaneja-Glaser\ndecomposition of a general element G of SU(2^N) in terms of its `Cartan\u0027 and\n`non-Cartan\u0027 components. This effectively factors G in terms of group elements\nthat belong in SU(2^n) with n\u003cN, a procedure that can be iterated down to n=2.\nWe show that every step reduces to solving the zeros of a matrix polynomial,\nobtained by truncation of the Baker-Campbell-Hausdorff formula, numerically.\nAll computational tasks involved are straightforward and the overall truncation\nerrors are well under control.",
"arxiv_id": "quant-ph/0505128",
"authors": [
"Henrique N. S\u00e1 Earp",
"Jiannis K. Pachos"
],
"categories": [
"quant-ph"
],
"doi": "10.1063/1.2008210",
"journal_ref": "Jour. Math. Phys. 46, 1 (2005)",
"title": "A constructive algorithm for the Cartan decomposition of SU(2^N)",
"url": "https://arxiv.org/abs/quant-ph/0505128"
},
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