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QFT

QFT(num_qubits=None, approximation_degree=0, do_swaps=True, inverse=False, insert_barriers=False, name=None) GitHub(opens in a new tab)

Bases: qiskit.circuit.library.blueprintcircuit.BlueprintCircuit

Quantum Fourier Transform Circuit.

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

j12n/2k=02n1e2πijk/2nk|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 (Optional[int]) – 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 (Optional[str]) – The name of the circuit.

Methods Defined Here

inverse

QFT.inverse()

Invert this circuit.

Return type

QFT

Returns

The inverted circuit.

is_inverse

QFT.is_inverse()

Whether the inverse Fourier transform is implemented.

Return type

bool

Returns

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


Attributes

ancillas

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

Return type

List[AncillaQubit]

approximation_degree

The approximation degree of the QFT.

Return type

int

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}}

Return type

dict

clbits

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

Return type

List[Clbit]

data

do_swaps

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

Return type

bool

Returns

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

extension_lib

= 'include "qelib1.inc";'

global_phase

Return the global phase of the circuit in radians.

Return type

Union[ParameterExpression, float]

= 'OPENQASM 2.0;'

insert_barriers

Whether barriers are inserted for better visualization or not.

Return type

bool

Returns

True, if barriers are inserted, False if not.

instances

= 9

metadata

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 type

dict

num_ancillas

Return the number of ancilla qubits.

Return type

int

num_clbits

Return number of classical bits.

Return type

int

num_parameters

Return type

int

num_qubits

The number of qubits in the QFT circuit.

Return type

int

Returns

The number of qubits in the circuit.

parameters

Return type

ParameterView

prefix

= 'circuit'

qregs

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.

Return type

List[Qubit]

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