A constructive algorithm for the Cartan decomposition of SU(2^N)
量子物理
2011-09-30 v2
摘要
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.
引用
@article{arxiv.quant-ph/0505128,
title = {A constructive algorithm for the Cartan decomposition of SU(2^N)},
author = {Henrique N. Sá Earp and Jiannis K. Pachos},
journal= {arXiv preprint arXiv:quant-ph/0505128},
year = {2011}
}
备注
15 pages, no figures, matlab file at http://cam.qubit.org/users/jiannis/