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

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 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):

Construct a new QFT circuit.
The class qiskit.circuit.library.basis_change.qft.QFT
is pending deprecation as of Qiskit 1.3. It will be marked deprecated in a future release, and then removed no earlier than 3 months after the release date. (‘Use qiskit.circuit.library.QFTGate or qiskit.synthesis.qft.synth_qft_full instead, for access to all previous arguments.’,)
Parameters
- 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.
Attributes
ancillas
A list of AncillaQubit
s in the order that they were added. You should not mutate this.
approximation_degree
The approximation degree of the QFT.
Returns
The currently set approximation degree.
clbits
A list of Clbit
s in the order that they were added. You should not mutate this.
Example
from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit
qr1 = QuantumRegister(2)
qr2 = QuantumRegister(1)
cr1 = ClassicalRegister(2)
cr2 = ClassicalRegister(1)
qc = QuantumCircuit(qr1, qr2, cr1, cr2)
print("List the qubits in this circuit:", qc.qubits)
print("List the classical bits in this circuit:", qc.clbits)
List the qubits in this circuit: [Qubit(QuantumRegister(2, 'q0'), 0),
Qubit(QuantumRegister(2, 'q0'), 1), Qubit(QuantumRegister(1, 'q1'), 0)]
List the classical bits in this circuit: [Clbit(ClassicalRegister(2, 'c0'), 0),
Clbit(ClassicalRegister(2, 'c0'), 1), Clbit(ClassicalRegister(1, 'c1'), 0)]
cregs
A list of Clbit
s in the order that they were added. You should not mutate this.
data
The circuit data (instructions and context).
Returns
a list-like object containing the CircuitInstruction
s for each instruction.
Return type
QuantumCircuitData
do_swaps
Whether the final swaps of the QFT are applied or not.
Returns
True, if the final swaps are applied, False if not.
duration
The total duration of the circuit, set by a scheduling transpiler pass. Its unit is specified by unit
.
The property qiskit.circuit.quantumcircuit.QuantumCircuit.duration
is deprecated as of Qiskit 1.3.0. It will be removed in Qiskit 3.0.0.
global_phase
The global phase of the current circuit scope in radians.
Example
from qiskit import QuantumCircuit
circuit = QuantumCircuit(2)
circuit.h(0)
circuit.cx(0, 1)
print(circuit.global_phase)
0.0
from numpy import pi
circuit.global_phase = pi/4
print(circuit.global_phase)
0.7853981633974483
insert_barriers
Whether barriers are inserted for better visualization or not.
Returns
True, if barriers are inserted, False if not.
instances
Default value: 223
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 that permutes the qubits based on the selected physical qubits on the Target
, and a final layout, which is an output permutation caused by SwapGate
s inserted during routing.
Example
from qiskit import QuantumCircuit
from qiskit.providers.fake_provider import GenericBackendV2
from qiskit.transpiler import generate_preset_pass_manager
# Create circuit to test transpiler on
qc = QuantumCircuit(3, 3)
qc.h(0)
qc.cx(0, 1)
qc.swap(1, 2)
qc.cx(0, 1)
# Add measurements to the circuit
qc.measure([0, 1, 2], [0, 1, 2])
# Specify the QPU to target
backend = GenericBackendV2(3)
# Transpile the circuit
pass_manager = generate_preset_pass_manager(
optimization_level=1, backend=backend
)
transpiled = pass_manager.run(qc)
# Print the layout after transpilation
print(transpiled.layout.routing_permutation())
[0, 1, 2]
metadata
Arbitrary user-defined dictionary of metadata for the circuit.
Qiskit will not examine the content of this mapping, but it will pass it through the transpiler and reattach it to the output, so you can track your own metadata.
Example
from qiskit import QuantumCircuit
qc = QuantumCircuit(2, 2, metadata={'experiment_type': 'Bell state experiment'})
print(qc.metadata)
{'experiment_type': 'Bell state experiment'}
num_ancillas
Return the number of ancilla qubits.
Example
from qiskit import QuantumCircuit, QuantumRegister, AncillaRegister
# Create a 2-qubit quantum circuit
reg = QuantumRegister(2)
qc = QuantumCircuit(reg)
# Create an ancilla register with 1 qubit
anc = AncillaRegister(1)
qc.add_register(anc) # Add the ancilla register to the circuit
print("Number of ancilla qubits:", qc.num_ancillas)
Number of ancilla qubits: 1
num_captured_stretches
The number of stretches in the circuit marked as captured from an enclosing scope.
This is the length of the iter_captured_stretches()
iterable. If this is non-zero, num_input_vars
must be zero.
num_captured_vars
The number of real-time classical variables in the circuit marked as captured from an enclosing scope.
This is the length of the iter_captured_vars()
iterable. If this is non-zero, num_input_vars
must be zero.
num_clbits
Return number of classical bits.
Example
from qiskit import QuantumCircuit
# Create a new circuit with two qubits and one classical bit
qc = QuantumCircuit(2, 1)
print("Number of classical bits:", qc.num_clbits)
Number of classical bits: 1
num_declared_stretches
The number of stretches in the circuit that are declared by this circuit scope, excluding captures.
This is the length of the iter_declared_stretches()
iterable.
num_declared_vars
The number of real-time classical variables in the circuit that are declared by this circuit scope, excluding inputs or captures.
This is the length of the iter_declared_vars()
iterable.
num_identifiers
The number of real-time classical variables and stretches in the circuit.
This is equal to num_vars()
+ num_stretches()
.
num_input_vars
The number of real-time classical variables in the circuit marked as circuit inputs.
This is the length of the iter_input_vars()
iterable. If this is non-zero, num_captured_vars
must be zero.
num_parameters
The number of parameter objects in the circuit.
num_qubits
The number of qubits in the QFT circuit.
Returns
The number of qubits in the circuit.
num_stretches
The number of stretches in the circuit.
This is the length of the iter_stretches()
iterable.
num_vars
The number of real-time classical variables in the circuit.
This is the length of the iter_vars()
iterable.
op_start_times
Return a list of operation start times.
This attribute computes the estimate starting time of the operations in the scheduled circuit and only works for simple circuits that have no control flow or other classical feed-forward operations.
This attribute is enabled once one of scheduling analysis passes runs on the quantum circuit.
Example
from qiskit import QuantumCircuit
from qiskit.providers.fake_provider import GenericBackendV2
from qiskit.transpiler import generate_preset_pass_manager
qc = QuantumCircuit(2)
qc.h(0)
qc.cx(0, 1)
qc.measure_all()
# Print the original circuit
print("Original circuit:")
print(qc)
# Transpile the circuit with a specific basis gates list and print the resulting circuit
backend = GenericBackendV2(2, basis_gates=['u1', 'u2', 'u3', 'cx'])
pm = generate_preset_pass_manager(
optimization_level=1, backend=backend, scheduling_method="alap"
)
transpiled_qc = pm.run(qc)
print("Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']:")
print(transpiled_qc)
# Print the start times of each instruction in the transpiled circuit
print("Start times of instructions in the transpiled circuit:")
for instruction, start_time in zip(transpiled_qc.data, transpiled_qc.op_start_times):
print(f"{instruction.operation.name}: {start_time}")
Original circuit:
┌───┐ ░ ┌─┐
q_0: ┤ H ├──■───░─┤M├───
└───┘┌─┴─┐ ░ └╥┘┌─┐
q_1: ─────┤ X ├─░──╫─┤M├
└───┘ ░ ║ └╥┘
meas: 2/══════════════╩══╩═
0 1
Transpiled circuit with basis gates ['u1', 'u2', 'u3', 'cx']:
┌─────────┐ ░ ┌─────────────────┐┌─┐
q_0 -> 0 ───┤ U2(0,π) ├──────■───░─┤ Delay(1255[dt]) ├┤M├
┌──┴─────────┴───┐┌─┴─┐ ░ └───────┬─┬───────┘└╥┘
q_1 -> 1 ┤ Delay(196[dt]) ├┤ X ├─░─────────┤M├─────────╫─
└────────────────┘└───┘ ░ └╥┘ ║
meas: 2/═══════════════════════════════════╩══════════╩═
1 0
Start times of instructions in the transpiled circuit:
u2: 0
delay: 0
cx: 196
barrier: 2098
delay: 2098
measure: 3353
measure: 2098
Returns
List of integers representing instruction estimated start times. The index corresponds to the index of instruction in QuantumCircuit.data
.
Raises
AttributeError – When circuit is not scheduled.
parameters
The parameters defined in the circuit.
This attribute returns the Parameter
objects in the circuit sorted alphabetically. Note that parameters instantiated with a ParameterVector
are still sorted numerically.
Examples
The snippet below shows that insertion order of parameters does not matter.
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> a, b, elephant = Parameter("a"), Parameter("b"), Parameter("elephant")
>>> circuit = QuantumCircuit(1)
>>> circuit.rx(b, 0)
>>> circuit.rz(elephant, 0)
>>> circuit.ry(a, 0)
>>> circuit.parameters # sorted alphabetically!
ParameterView([Parameter(a), Parameter(b), Parameter(elephant)])
Bear in mind that alphabetical sorting might be unintuitive when it comes to numbers. The literal “10” comes before “2” in strict alphabetical sorting.
>>> from qiskit.circuit import QuantumCircuit, Parameter
>>> angles = [Parameter("angle_1"), Parameter("angle_2"), Parameter("angle_10")]
>>> circuit = QuantumCircuit(1)
>>> circuit.u(*angles, 0)
>>> circuit.draw()
┌─────────────────────────────┐
q: ┤ U(angle_1,angle_2,angle_10) ├
└─────────────────────────────┘
>>> circuit.parameters
ParameterView([Parameter(angle_1), Parameter(angle_10), Parameter(angle_2)])
To respect numerical sorting, a ParameterVector
can be used.
>>> from qiskit.circuit import QuantumCircuit, Parameter, ParameterVector
>>> x = ParameterVector("x", 12)
>>> circuit = QuantumCircuit(1)
>>> for x_i in x:
... circuit.rx(x_i, 0)
>>> circuit.parameters
ParameterView([
ParameterVectorElement(x[0]), ParameterVectorElement(x[1]),
ParameterVectorElement(x[2]), ParameterVectorElement(x[3]),
..., ParameterVectorElement(x[11])
])
Returns
The sorted Parameter
objects in the circuit.
prefix
Default value: 'circuit'
qregs
A list of the quantum registers associated with the circuit.
qubits
A list of Qubit
s in the order that they were added. You should not mutate this.
unit
The unit that duration
is specified in.
The property qiskit.circuit.quantumcircuit.QuantumCircuit.unit
is deprecated as of Qiskit 1.3.0. It will be removed in Qiskit 3.0.0.
name
Type: str
A human-readable name for the circuit.
Example
from qiskit import QuantumCircuit
qc = QuantumCircuit(2, 2, name="my_circuit")
print(qc.name)
my_circuit
Methods
inverse
inverse(annotated=False)
Invert this circuit.
Parameters
annotated (bool) – indicates whether the inverse gate can be implemented as an annotated gate. The value of this argument is ignored as the inverse of a QFT is an IQFT which is just another instance of QFT
.
Returns
The inverted circuit.
Return type
is_inverse
is_inverse()
Whether the inverse Fourier transform is implemented.
Returns
True, if the inverse Fourier transform is implemented, False otherwise.
Return type