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Suppose we have a matrix $A=\begin{bmatrix} 2 &4 \\ 1 & 4\\ \end{bmatrix}$, when applying the discrete wavelet transform to this matrix we get 4 parts i.e smooth part ($1\times 1$) matrix, 3 detail parts each of them being ($1\times 1$) matrices. Is there any quantum transformation that performs this task? Can somebody suggest? Is it in some way related to Fourier Transformation?

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  • $\begingroup$ Could you expand a bit more? $\endgroup$ – AHusain Apr 8 at 15:47
  • $\begingroup$ what part do you want me to expand? $\endgroup$ – Upstart Apr 8 at 16:39
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    $\begingroup$ You seem to be using non-standard terminology with detail parts etc so follow through with your example A. $\endgroup$ – AHusain Apr 8 at 18:49
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This paper by Andreas Klappenecker might be a good starting point. The paper spearheaded quantum wavelet transforms and so-called wavelet packet transforms. A wavelet packet transforms yields an iterated decomposition into high-pass and low-pass filtered signals, whereas a wavelet transform only further decomposes the low-pass filtered and down-scaled version of the signal.

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