Question

I try to make a Quantum Fourier Transformation with N=6:

w=e^(2*pi*7/6)
so we have 6-th roots: 1,w,w^2,-1,-w,-w^2

My matrix is QFT6= 1/sqrt(6)*

(1 1 1 1 1 1 )
(1 w w^2 -1 -w -w^2)
(1 w^2 -w 1 w^2 -w )
(1 -1 1 -1 1 -1 )
(1 -w w^2 1 -w w^2 )
(1 -w^2 -w -1 w^2 w )

the vector that should be transformed is: 1/sqrt(2)* (|1> + |4>)
=1/sqrt(2)*(0 1 0 0 1 0)^T

if I multiply I get:

1/sqrt(3)*(1 0 w^2 0 -w 0)^T

there must be a mistake but I do not find it..

Answer 1

sorry.. w=e^(2*pi*i/6)
that was not the mistake just a type error ;)

Answer 2

the matrix u get
1/sqrt(3)*(1,0,w^2,0'-w,0)is right