# QFT

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

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:

The inverse QFT can be obtained by calling the `inverse`

method on this class. The respective circuit diagram is:

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(opens in a new tab) or https://arxiv.org/abs/quant-ph/0403071(opens in a new tab).

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):

Construct a new QFT circuit.

**Parameters**

**num_qubits**(*int*(opens in a new tab)*| None*) – The number of qubits on which the QFT acts.**approximation_degree**(*int*(opens in a new tab)) – The degree of approximation (0 for no approximation).**do_swaps**(*bool*(opens in a new tab)) – Whether to include the final swaps in the QFT.**inverse**(*bool*(opens in a new tab)) – If True, the inverse Fourier transform is constructed.**insert_barriers**(*bool*(opens in a new tab)) – If True, barriers are inserted as visualization improvement.**name**(*str*(opens in a new tab)*| 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}}`

### clbits

A list of `Clbit`

s in the order that they were added. You should not mutate this.

### data

### do_swaps

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

**Returns**

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

### 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: `214`

### layout

Return any associated layout information about the circuit

This attribute contains an optional `TranspileLayout`

object. This is typically set on the output from `transpile()`

or `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()`

function, an initial layout which permutes the qubits based on the selected physical qubits on the `Target`

, and a final layout which is an output permutation caused by `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`

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`

must be zero.

### num_parameters

### 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**(opens in a new tab) – When circuit is not scheduled.

### parameters

### 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.

### 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.

### duration

Type: `int | float | None`

The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by `unit`

.

### unit

The unit that `duration`

is specified in.

## Methods

### inverse

`inverse(annotated=False)`

Invert this circuit.

**Parameters**

**annotated** (*bool*(opens in a new tab)) – 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`

.

**Returns**

The inverted circuit.

**Return type**

### is_inverse

`is_inverse()`

Whether the inverse Fourier transform is implemented.

**Returns**

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

**Return type**