# Train a diagonal unitary matrix？

\left[ \begin{array}{*{35}{l}} 1 & {} & {} & {} & {} & {} & {} & {} \\ {} & -1 & {} & {} & {} & {} & {} & {} \\ {} & {} & 1 & {} & {} & {} & {} & {} \\ {} & {} & {} & 1 & {} & {} & {} & {} \\ {} & {} & {} & {} & -1 & {} & {} & {} \\ {} & {} & {} & {} & {} & 1 & {} & {} \\ {} & {} & {} & {} & {} & {} & -1 & {} \\ {} & {} & {} & {} & {} & {} & {} & 1 \\ \end{array} \right]
is the initial diagonalunitary matrix. \left[ \begin{array}{*{35}{l}} 1 & {} & {} & {} & {} & {} & {} & {} \\ {} & -1 & {} & {} & {} & {} & {} & {} \\ {} & {} & -1 & {} & {} & {} & {} & {} \\ {} & {} & {} & -1 & {} & {} & {} & {} \\ {} & {} & {} & {} & -1 & {} & {} & {} \\ {} & {} & {} & {} & {} & 1 & {} & {} \\ {} & {} & {} & {} & {} & {} & -1 & {} \\ {} & {} & {} & {} & {} & {} & {} & 1 \\ \end{array} \right]
is the target diagonalunitary matrix. How can we ensure that each iteration produces a diagonalunitary matrix? End up with \left[ \begin{array}{*{35}{l}} 1 & {} & {} & {} & {} & {} & {} & {} \\ {} & -1 & {} & {} & {} & {} & {} & {} \\ {} & {} & -1 & {} & {} & {} & {} & {} \\ {} & {} & {} & -1 & {} & {} & {} & {} \\ {} & {} & {} & {} & -1 & {} & {} & {} \\ {} & {} & {} & {} & {} & 1 & {} & {} \\ {} & {} & {} & {} & {} & {} & -1 & {} \\ {} & {} & {} & {} & {} & {} & {} & 1 \\ \end{array} \right]. That is, the output of each iteration step can be obtained as a diagonal unitary matrix according to the parameters. Is this trainable? Please show Dome.

I leave here the reference to the other conversation