QFT
class QFT(num_qubits=None, approximation_degree=0, do_swaps=True, inverse=False, insert_barriers=False, name=None)
Bases: qiskit.circuit.library.blueprintcircuit.BlueprintCircuit
Quantum Fourier Transform Circuit.
The Quantum Fourier Transform (QFT) on qubits is the operation
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)
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)
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)
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
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
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
Default value: 'include "qelib1.inc";'
global_phase
header
Default value: '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
Default value: 2445
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.
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.
Return type
List[int]
Returns
List of integers representing instruction start times. The index corresponds to the index of instruction in QuantumCircuit.data.
Raises
AttributeError – When circuit is not scheduled.
parameters
Return type
ParameterView
prefix
Default value: 'circuit'
qregs
A list of the quantum registers associated with the circuit.