  In this work we present a method of decomposition of arbitrary unitary matrix
$U\in\mathbf U(2^k)$ into a product of single-qubit negator and
controlled-$\sqrt{\mbox{NOT}}$ gates. Since the product results with negator
matrix, which can be treated as complex analogue if bistochastic matrix, our
method can be seen as complex analogue of Sinkhorn-Knopp algorithm, where
diagonal matrices are replaced by adding and removing an one-qubit ancilla. The
decomposition can be found constructively and resulting circuit consists of
$O(4^k)$ entangling gates, which is proved to be optimal. An example of such
transformation is presented.
