The iterative method of Sinkhorn allows, starting from an arbitrary real
matrix with non-negative entries, to find a so-called 'scaled matrix' which is
doubly stochastic, i.e. a matrix with all entries in the interval (0, 1) and
with all line sums equal to 1. We conjecture that a similar procedure exists,
which allows, starting from an arbitrary unitary matrix, to find a scaled
matrix which is unitary and has all line sums equal to 1. The existence of such
algorithm guarantees a powerful decomposition of an arbitrary quantum circuit.Comment: A proof of the conjecture is now provided by Idel & Wolf
(http://arxiv.org/abs/1408.5728
