> ## Documentation Index
> Fetch the complete documentation index at: https://prod-mint.classiq.io/llms.txt
> Use this file to discover all available pages before exploring further.

# Quantum Fourier Transform

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  Open this notebook in GitHub to run it yourself
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The quantum Fourier transform (QFT) function is the quantum analog for
discrete Fourier transform. It is applied on the quantum register state vector.

The state vector `x` is transformed to `y` in the following manner:

$$
y_{k} = \frac{1}{\sqrt{N}} \sum_{j=0}^{N-1} x_j e^{2\pi i \frac{jk}{N}}
$$

Function: `qft`

Arguments:

* `target`: `QArray[QBit]`

The `target` quantum argument is the quantum state on which we apply the QFT.

## Example

```python theme={null}
from classiq import *


@qfunc
def main(x: Output[QArray[QBit]]):
    allocate(4, x)
    qft(x)


qmod = create_model(main)
```

```python theme={null}

qprog = synthesize(qmod)
```