  A quantum compiler is a software program for decomposing ("compiling") an
arbitrary unitary matrix into a sequence of elementary operations (SEO).
Coppersmith showed that the $\nb$-bit Discrete Fourier Transform matrix
$U_{FT}$ can be decomposed in a very efficient way, as a sequence of
order($\nb^2$) elementary operations. Can a quantum compiler that doesn't know
a priori about Coppersmith's decomposition nevertheless decompose $U_{FT}$ as a
sequence of order($\nb^2$) elementary operations? In other words, can it
rediscover Coppersmith's decomposition by following a much more general
algorithm? Yes it can, if that more general algorithm is the recursive
application of the Cosine-Sine Decomposition (CSD).

Quantum Physics