QFT¶

class 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, png, hires.png, pdf)

../_images/qiskit-circuit-library-QFT-1.png

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

(Source code, png, hires.png, pdf)

../_images/qiskit-circuit-library-QFT-2.png

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, png, hires.png, pdf)

../_images/qiskit-circuit-library-QFT-3.png

Construct a new QFT circuit.

Paramètres

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`	Invert this circuit.
`is_inverse`	Whether the inverse Fourier transform is implemented.

Attributes

ancillas¶

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

Type renvoyé: List[AncillaQubit]

approximation_degree¶

The approximation degree of the QFT.

Type renvoyé: int
Renvoie: 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}}

Type renvoyé: dict

clbits¶

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

Type renvoyé: List[Clbit]

data¶

do_swaps¶

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

Type renvoyé: bool
Renvoie: 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.

Type renvoyé: Union[ParameterExpression, float]

header = 'OPENQASM 2.0;'¶

insert_barriers¶

Whether barriers are inserted for better visualization or not.

Type renvoyé: bool
Renvoie: True, if barriers are inserted, False if not.

instances = 2153¶

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.

Type renvoyé: dict

num_ancillas¶

Return the number of ancilla qubits.

Type renvoyé: int

num_clbits¶

Return number of classical bits.

Type renvoyé: int

num_parameters¶

Type renvoyé: int

num_qubits¶

The number of qubits in the QFT circuit.

Type renvoyé: int
Renvoie: 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.

Type renvoyé: List[int]
Renvoie: List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.
Lève: AttributeError – When circuit is not scheduled.

parameters¶

Type renvoyé: 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.

Type renvoyé: List[Qubit]