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

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:

(Source code)


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

(Source code)


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 or 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):

(Source code)


Construct a new QFT circuit.

  • num_qubits (int | None) – The number of qubits on which the QFT acts.

  • approximation_degree (int) – The degree of approximation (0 for no approximation).

  • do_swaps (bool) – Whether to include the final swaps in the QFT.

  • inverse (bool) – If True, the inverse Fourier transform is constructed.

  • insert_barriers (bool) – If True, barriers are inserted as visualization improvement.

  • name (str | None) – The name of the circuit.



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


The approximation degree of the QFT.


The currently set approximation degree.


Return calibration dictionary.

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


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


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


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

extension_lib = 'include "qelib1.inc";'#

Return the global phase of the circuit in radians.

header = 'OPENQASM 2.0;'#

Whether barriers are inserted for better visualization or not.


True, if barriers are inserted, False if not.

instances = 264#

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.


Return the number of ancilla qubits.


Return number of classical bits.


The number of qubits in the QFT circuit.


The number of qubits in the circuit.


Return a list of operation start times.

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


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


AttributeError – When circuit is not scheduled.

prefix = 'circuit'#
qregs: list[QuantumRegister]#

A list of the quantum registers associated with the circuit.


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



Invert this circuit.


The inverted circuit.

Return type:



Whether the inverse Fourier transform is implemented.


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

Return type: