Quantum Fourier Transform

Let's discover a little bit more about the Fourier Transform (FT) and QFT.

FT is a mathematical function. It can be intuitively thought of like a musical chord in terms of volume and frequency. The FT can transform an original function into another function, representing the amount of frequency present in the original function. The FT depends on the spatial or temporal frequency and is referred to as a time domain. It is represented by a graphic that shows the frequency that was detected, as shown in the following diagram:

Figure 8.14 – Fourier Transform

To understand how this works, let's look at an example of FT taking an arithmetic succession of numbers, like so:

1, 3, 7, 2, 1, 3, 7, 2

As you can see, we have the first four numbers – 1, 3, 7, 2 – which get repeated two times. In other words, we can break the succession into two parts:

1,3,7,2 | 1,3,7,2

Note

The | symbol represents...