30 lines
690 B
Markdown
30 lines
690 B
Markdown
A mathematical technique that decomposes a function into its constituent frequencies.
|
|
|
|
## Definition
|
|
![[Pasted image 20260730181449.png]]
|
|
|
|
The transformation is a process that takes a periodic vector as an input and outputs
|
|
the period of that vector.
|
|
|
|
![[Pasted image 20260730181941.png]]
|
|
|
|
## Construction
|
|
|
|
We will now model DFT as a quantum circuit.
|
|
For this we only look at N = $2^n$, DFT applied on n qubits.
|
|
|
|
![[Pasted image 20260730182117.png]]
|
|
|
|
Let us look at an example DFT for n = 3:
|
|
![[Pasted image 20260730183136.png]]
|
|
![[Pasted image 20260730183145.png]]
|
|
|
|
|
|
The more general approach works as follows:
|
|
|
|
![[Pasted image 20260730185053.png]]
|
|
|
|
![[Pasted image 20260730185144.png]]
|
|
|
|
|