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# QFT

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

GitHub(opens in a new tab)

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

## Attributes

### ancillas

Returns a list of ancilla bits in the order that the registers were added.

### 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

Returns a list of classical bits in the order that the registers were added.

### do_swaps

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

Returns

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

### extension_lib

Default value: 'include "qelib1.inc";'

### global_phase

Return the global phase of the current circuit scope in radians.

Default value: 'OPENQASM 2.0;'

### insert_barriers

Whether barriers are inserted for better visualization or not.

Returns

True, if barriers are inserted, False if not.

### instances

Default value: 226

### 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 SwapGates inserted during routing.

The user provided metadata associated with the circuit.

The metadata for the circuit is a user provided dict of metadata for the circuit. It will not be used to influence the execution or operation of the circuit, but it is expected to be passed between all transforms of the circuit (ie transpilation) and that providers will associate any circuit metadata with the results it returns from execution of that circuit.

### num_ancillas

Return the number of ancilla qubits.

### num_clbits

Return number of classical bits.

### num_qubits

The number of qubits in the QFT circuit.

Returns

The number of qubits in the circuit.

### 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.

### prefix

Default value: 'circuit'

### qregs

Type: list[QuantumRegister]

A list of the quantum registers associated with the circuit.

### qubits

Returns a list of quantum bits in the order that the registers were added.

## Methods

### inverse

inverse()

Invert this circuit.

Returns

The inverted circuit.

Return type

QFT

### is_inverse

is_inverse()

Whether the inverse Fourier transform is implemented.

Returns

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

Return type

bool(opens in a new tab)