I'm self learning quantum computing through IBM's Qiskit's learning section (which I really like), and I've stumbled across an inequality that I don't quite understand fully.
This must be really easy, I just don't get this next inequality.
In their of the QFT circuit implementation, they write:
What interests me is the last equation, and specifically in the last equation the
x circled in blue. This interest me because of their next proof of the QFT's circuit implementation:
Again, the last equation is what interests me.
Disregarding the order of qubits (Which I know is reversed in the equations), I do not understand how the first picture
x's are equal to the second picture
For example, in their example for a 3-qubit QFT, their output of the circuit is as follows: Which is to my understanding not equal to their equation in the first picture (Focusing on the
x's - in the first picture the
x's are complete in each tensor product of the equation while in the last its only
x's partial components in each tensor product).