Chi-Kwong Li, Xiaoyan Yin
It is shown that every $d$-by-$d$ unitary matrix can be written as the product of two-level unitary matrices with special structure and prescribed determinants. The result is then applied to show that every unitary gate acting on $n$-qubit register can be expressed as no more than $2^n(2^n-1)/2$ controlled single qubit gates chosen from $2^n-1$ classes so that matrices in each class share the same $n-1$ control qubits. Related results are discussed.
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http://arxiv.org/abs/1210.7366
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