Now, I am working on a quantum supervised learning problem and I have a problem with amplitude encoding.
Before being encoded, a vector $(a_1, a_2,\dots,a_n)$ must be normalized in such a way that $\sum_i |a_i|^2 = 1$
Thereby, the two following vectors would be encoded in the same way : $(1, 2, 3, 4)$ and $(2, 4, 6, 8)$ normalized as $(0.18, 0.36, 0.54, 0.73)$ :
$0.18\lvert 00\rangle + 0.36\lvert 01\rangle + 0.54\lvert 10\rangle + 0.73\lvert 11\rangle$.
But in the case of a classification/regression problem I could have a different target for this two vectors and my circuit would not be able to treat them differently.
Is there a way to normalize/encode vectors differently to keep a difference between colinear vectors ?
[Edit :] the final goal is to make a regression model based on a variational circuit as explained on this website but for a different problem : http://docs.qulacs.org/en/latest/apply/5.2_qcl.html