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This page will contain a list of an exhaustive list of unitary matrices decomposition.

Factorization of unitary matrices

List of known unitary matrices decompositions. Simple factorization of unitary transformations by Hubert de Guise, Olivia Di Matteo, and Luis L. Sánchez-Soto. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.022328.

The canonical coset decomposition of unitary matrices through Householder transformations by Renan Cabreraa), Traci Strohecker, and Herschel Rabitz. https://aip.scitation.org/doi/10.1063/1.3466798 Note: this decomposition only requires $N$ terms. Note: There is an apparent error in matrix $\vert R\rangle_{\vert U_2\rangle}$: entry $3,1$ must be $$ \frac{2+\sqrt{2}}{4}. $$

Factorization of unitary matrices by P Dita. https://iopscience.iop.org/article/10.1088/0305-4470/36/11/309 Note: I used this one when searching unistochastic channels. My numerical method worked better with this one.

Random Unitary matrices by K Zyczkowski and M Kus https://iopscience.iop.org/article/10.1088/0305-4470/27/12/028/meta Note: In this paper there is a reference to another one by Hurwitz. However, I was not able to find it, so I quote it. Also, the explanation is good.

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start.txt · Last modified: 2020/11/22 20:38 by david