Geodesic
On the complexity of unitary transformations
Diskretnaya Matematika, Tome 15 (2003) no. 4, pp. 113-118

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In this paper, we suggest a method to derive lower bounds for the complexity of non-branching programs whose elementary operations are unitary transformations over two complex numbers. This method provides us with estimates of the form $\Omega(n\log n)$ for unitary operators $\mathbf C^n\to\mathbf C^n$, in particular, for the Fourier and Walsh transformations. For $n=2^k$ we find precise values of the complexity of those transformations. This research was supported by the Russian Foundation for Basic Research, grant 00–15–96103. 
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     author = {D. Yu. Cherukhin},
     title = {On the complexity of unitary transformations},
     journal = {Diskretnaya Matematika},
     pages = {113--118},
     publisher = {mathdoc},
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     number = {4},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DM_2003_15_4_a6/}
}
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D. Yu. Cherukhin. On the complexity of unitary transformations. Diskretnaya Matematika, Tome 15 (2003) no. 4, pp. 113-118. http://geodesic.mathdoc.fr/item/DM_2003_15_4_a6/