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Quantum Fourier Transform

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:

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

Syntax

Function: QFT

Parameters:

  • num_qubits: PositiveInt
  • approximation_degree: NonNegativeInt
  • do_swaps: bool

The approximation_degree attribute omits rotation gates for small angles. The default value is 0.

The do_swaps attribute adds additional SWP gates after the QFT, thereby reversing the order of the qubits. The default value is True.

Example

{
  "functions": [
    {
      "name": "main",
      "body": [
          {
              "function": "QFT",
              "function_params": {
                  "num_qubits": 4
              }
          }
      ]
    }
  ]
}

from classiq.builtin_functions import QFT
from classiq import Model, synthesize

model = Model()
params = QFT(
    num_qubits=4,
)
model.QFT(params)
quantum_program = synthesize(model.get_model())

QFT_Example