ABC matrices for multi-controlled unitary

[IsmaelCesar]

Co-Authored-By: @IsmaelCesar
Co-Authored-By: @cab4
Co-Authored-By: @Augusto12
Co-Authored-By: @adjs

Summary

Issue #5872
Changing the multi-controlled gate based on lemma 7.9 and corollary 7.4 from arXiv:quant-ph/9503016v1

Details and comments

Instead of three multi-controlled gates $R_z$, $R_y$ and $R_z$, using the unitary $U$ to be applied to the circuit by decomposing it into three gates $A$, $B$ and $C$ where $ABC = I$. And also using a multi-controlled phase gate to apply the local phase of the unitary: $e^{i\alpha}$

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