---
title: QFT (v1.3)
description: API reference for qiskit.circuit.library.QFT in qiskit v1.3
source: https://eu-de.quantum.cloud.ibm.com/docs/en/api/qiskit/1.3/qiskit.circuit.library.QFT
---

# QFT

*class* `qiskit.circuit.library.QFT(num_qubits=None, approximation_degree=0, do_swaps=True, inverse=False, insert_barriers=False, name=None)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/basis_change/qft.py#L23-L279)

Bases: `BlueprintCircuit`

Quantum Fourier Transform Circuit.

The Quantum Fourier Transform (QFT) on $n$ qubits is the operation

$$
|j\rangle \mapsto \frac{1}{2^{n/2}} \sum_{k=0}^{2^n - 1} e^{2\pi ijk / 2^n} |k\rangle
$$

The circuit that implements this transformation can be implemented using Hadamard gates on each qubit, a series of controlled-U1 (or Z, depending on the phase) gates and a layer of Swap gates. The layer of Swap gates can in principle be dropped if the QFT appears at the end of the circuit, since then the re-ordering can be done classically. They can be turned off using the `do_swaps` attribute.

For 4 qubits, the circuit that implements this transformation is:

![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/1.3/qiskit-circuit-library-QFT-1.avif)

The inverse QFT can be obtained by calling the `inverse` method on this class. The respective circuit diagram is:

![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/1.3/qiskit-circuit-library-QFT-2.avif)

One method to reduce circuit depth is to implement the QFT approximately by ignoring controlled-phase rotations where the angle is beneath a threshold. This is discussed in more detail in [https://arxiv.org/abs/quant-ph/9601018](https://arxiv.org/abs/quant-ph/9601018) or [https://arxiv.org/abs/quant-ph/0403071](https://arxiv.org/abs/quant-ph/0403071).

Here, this can be adjusted using the `approximation_degree` attribute: the smallest `approximation_degree` rotation angles are dropped from the QFT. For instance, a QFT on 5 qubits with approximation degree 2 yields (the barriers are dropped in this example):

![Diagram illustrating the previously described circuit.](https://eu-de.quantum.cloud.ibm.com/docs/images/api/qiskit/1.3/qiskit-circuit-library-QFT-3.avif)

Construct a new QFT circuit.

> **Deprecated since version 1.3\_pending**
>
> The class `qiskit.circuit.library.basis_change.qft.QFT` is pending deprecation as of qiskit 1.3. It will be marked deprecated in a future release, and then removed no earlier than 3 months after the release date. (‘Use qiskit.circuit.library.QFTGate or qiskit.synthesis.qft.synth\_qft\_full instead, for access to all previous arguments.’,)

**Parameters**

- **num\_qubits** ([*int*](https://docs.python.org/3/library/functions.html#int) *| None*) – The number of qubits on which the QFT acts.
- **approximation\_degree** ([*int*](https://docs.python.org/3/library/functions.html#int)) – The degree of approximation (0 for no approximation).
- **do\_swaps** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – Whether to include the final swaps in the QFT.
- **inverse** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If True, the inverse Fourier transform is constructed.
- **insert\_barriers** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – If True, barriers are inserted as visualization improvement.
- **name** ([*str*](https://docs.python.org/3/library/stdtypes.html#str) *| None*) – The name of the circuit.

## Attributes

### ancillas

A list of `AncillaQubit`s in the order that they were added. You should not mutate this.

### approximation\_degree

The approximation degree of the QFT.

**Returns**

The currently set approximation degree.

### calibrations

Return calibration dictionary.

The custom pulse definition of a given gate is of the form `{'gate_name': {(qubits, params): schedule}}`

> **Deprecated since version 1.3**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations` is deprecated as of Qiskit 1.3. It will be removed in Qiskit 2.0. The entire Qiskit Pulse package is being deprecated and will be moved to the Qiskit Dynamics repository: [https://github.com/qiskit-community/qiskit-dynamics](https://github.com/qiskit-community/qiskit-dynamics). Note that once removed, `qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations` will have no alternative in Qiskit.

### clbits

A list of `Clbit`s in the order that they were added. You should not mutate this.

### data

The circuit data (instructions and context).

**Returns**

a list-like object containing the [`CircuitInstruction`](/docs/api/qiskit/1.3/qiskit.circuit.CircuitInstruction "qiskit.circuit.CircuitInstruction")s for each instruction.

**Return type**

QuantumCircuitData

### do\_swaps

Whether the final swaps of the QFT are applied or not.

**Returns**

True, if the final swaps are applied, False if not.

### duration

The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by [`unit`](#qiskit.circuit.library.QFT.unit "qiskit.circuit.library.QFT.unit").

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.duration` is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.

### global\_phase

The global phase of the current circuit scope in radians.

### insert\_barriers

Whether barriers are inserted for better visualization or not.

**Returns**

True, if barriers are inserted, False if not.

### instances

Default value: `160`

### layout

Return any associated layout information about the circuit

This attribute contains an optional [`TranspileLayout`](/docs/api/qiskit/1.3/qiskit.transpiler.TranspileLayout "qiskit.transpiler.TranspileLayout") object. This is typically set on the output from [`transpile()`](/docs/api/qiskit/1.3/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") or [`PassManager.run()`](/docs/api/qiskit/1.3/qiskit.transpiler.PassManager#run "qiskit.transpiler.PassManager.run") to retain information about the permutations caused on the input circuit by transpilation.

There are two types of permutations caused by the [`transpile()`](/docs/api/qiskit/1.3/compiler#qiskit.compiler.transpile "qiskit.compiler.transpile") function, an initial layout which permutes the qubits based on the selected physical qubits on the [`Target`](/docs/api/qiskit/1.3/qiskit.transpiler.Target "qiskit.transpiler.Target"), and a final layout which is an output permutation caused by [`SwapGate`](/docs/api/qiskit/1.3/qiskit.circuit.library.SwapGate "qiskit.circuit.library.SwapGate")s inserted during routing.

### metadata

Arbitrary user-defined metadata for the circuit.

Qiskit will not examine the content of this mapping, but it will pass it through the transpiler and reattach it to the output, so you can track your own metadata.

### num\_ancillas

Return the number of ancilla qubits.

### num\_captured\_vars

The number of real-time classical variables in the circuit marked as captured from an enclosing scope.

This is the length of the `iter_captured_vars()` iterable. If this is non-zero, [`num_input_vars`](#qiskit.circuit.library.QFT.num_input_vars "qiskit.circuit.library.QFT.num_input_vars") must be zero.

### num\_clbits

Return number of classical bits.

### num\_declared\_vars

The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.

This is the length of the `iter_declared_vars()` iterable.

### num\_input\_vars

The number of real-time classical variables in the circuit marked as circuit inputs.

This is the length of the `iter_input_vars()` iterable. If this is non-zero, [`num_captured_vars`](#qiskit.circuit.library.QFT.num_captured_vars "qiskit.circuit.library.QFT.num_captured_vars") must be zero.

### num\_parameters

The number of parameter objects in the circuit.

### num\_qubits

The number of qubits in the QFT circuit.

**Returns**

The number of qubits in the circuit.

### num\_vars

The number of real-time classical variables in the circuit.

This is the length of the `iter_vars()` iterable.

### op\_start\_times

Return a list of operation start times.

This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.

**Returns**

List of integers representing instruction start times. The index corresponds to the index of instruction in `QuantumCircuit.data`.

**Raises**

[**AttributeError**](https://docs.python.org/3/library/exceptions.html#AttributeError) – When circuit is not scheduled.

### parameters

The parameters defined in the circuit.

This attribute returns the [`Parameter`](/docs/api/qiskit/1.3/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit sorted alphabetically. Note that parameters instantiated with a [`ParameterVector`](/docs/api/qiskit/1.3/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") are still sorted numerically.

**Examples**

The snippet below shows that insertion order of parameters does not matter.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters  # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])
```

Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
   ┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
   └─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])
```

To respect numerical sorting, a [`ParameterVector`](/docs/api/qiskit/1.3/qiskit.circuit.ParameterVector "qiskit.circuit.ParameterVector") can be used.

```python
>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
...     circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
    ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
    ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
    ..., ParameterVectorElement(x[11])
])
```

**Returns**

The sorted [`Parameter`](/docs/api/qiskit/1.3/qiskit.circuit.Parameter "qiskit.circuit.Parameter") objects in the circuit.

### prefix

Default value: `'circuit'`

### qregs

Type: `list[QuantumRegister]`

A list of the `QuantumRegister`s in this circuit. You should not mutate this.

### qubits

A list of `Qubit`s in the order that they were added. You should not mutate this.

### unit

The unit that [`duration`](#qiskit.circuit.library.QFT.duration "qiskit.circuit.library.QFT.duration") is specified in.

> **Deprecated since version 1.3.0**
>
> The property `qiskit.circuit.quantumcircuit.QuantumCircuit.unit` is deprecated as of qiskit 1.3.0. It will be removed in Qiskit 2.0.0.

### name

Type: `str`

A human-readable name for the circuit.

### cregs

Type: `list[ClassicalRegister]`

A list of the `ClassicalRegister`s in this circuit. You should not mutate this.

## Methods

### inverse

`inverse(annotated=False)`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/basis_change/qft.py#L216-L244)

Invert this circuit.

**Parameters**

**annotated** ([*bool*](https://docs.python.org/3/library/functions.html#bool)) – indicates whether the inverse gate can be implemented as an annotated gate. The value of this argument is ignored as the inverse of a QFT is an IQFT which is just another instance of [`QFT`](#qiskit.circuit.library.QFT "qiskit.circuit.library.QFT").

**Returns**

The inverted circuit.

**Return type**

[*QFT*](#qiskit.circuit.library.QFT "qiskit.circuit.library.basis_change.qft.QFT")

### is\_inverse

`is_inverse()`

[GitHub](https://github.com/Qiskit/qiskit/tree/stable/1.3/qiskit/circuit/library/basis_change/qft.py#L208-L214)

Whether the inverse Fourier transform is implemented.

**Returns**

True, if the inverse Fourier transform is implemented, False otherwise.

**Return type**

[bool](https://docs.python.org/3/library/functions.html#bool)