Exploring the QFT
In the previous section, we saw that the classical DFT is a mapping process or a transformation of a function from one domain to another. In a very similar way, the QFT is a transformation of the quantum states from the Z basis to the X basis (the Hadamard basis). Now, you might recall that the Hadamard gate that you saw in Chapter 2, Quantum Bits, Quantum Measurements, and Quantum Logic Gates, did the same operation. Yes, you are absolutely right in thinking that because the Hadamard operation is the one-qubit QFT!
The QFT performs a DFT operation but not on a classical sequence, rather on a quantum state. The QFT is an important algorithm to study as it is used as a subroutine for other quantum algorithms, such as the quantum phase estimation algorithm, which we will be discussing later in this chapter.
Mathematically, the QFT transformation is defined as follows:
Now, the formula for 
is provided as follows:
In the equations...
