In lesson 16 on the Quantum fourier Transform, the Sharma tutorial offers
something quite useful: a visual representation of numbers 1 to 15 in the binary
state on Bloch Spheres. Followed by, also on Bloch spheres, these same numbers
in the Fouriers Basis ie as angular turns around the Z-axis once a Hadamard
gate has been applied.
For the binaries. Below, the number 13:
The left most flips once at every increment, with the number 1 at down. The
second flips every 2 with first flip toward up, the third at every 4 , the fourth
at every 8. All works just like the progression of binary numbers:
Checking if our number 13 is correct, notice we are in reverse order with the most significant
number at the end.
On the Fourier Basis:
Each increment is 1/16th of a full turn on the Hadamard plane. Thus, for 13
13/16 full turns, 1 full turn with remainder10, 3 full turns with remainder 4,
and 6 full turns with remainder 8. Again, the most significant value is at the end.
Have yet to put this on qiskit, with updated code...
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