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 AncillaQubits 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.
calibrations
Return calibration dictionary.
The custom pulse definition of a given gate is of the form {'gate_name': {(qubits, params): schedule}}
The property qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations is deprecated as of Qiskit 1.3. It will be removed in Qiskit 2.0. The entire Qiskit Pulse package is being deprecated and will be moved to the Qiskit Dynamics repository: https://github.com/qiskit-community/qiskit-dynamics. Note that once removed, qiskit.circuit.quantumcircuit.QuantumCircuit.calibrations will have no alternative in Qiskit.
clbits
A list of Clbits 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 CircuitInstructions 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 2.0.0.
global_phase
The global phase of the current circuit scope in radians.
insert_barriers
Whether barriers are inserted for better visualization or not.
Returns
True, if barriers are inserted, False if not.
instances
Default value: 160
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 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.
metadata
Arbitrary user-defined 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.
num_ancillas
Return the number of ancilla qubits.
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.
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_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_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 is enabled once one of scheduling analysis passes runs on the quantum circuit.
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
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
Type: list[QuantumRegister]
A list of the QuantumRegisters in this circuit. You should not mutate this.
qubits
A list of Qubits 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 2.0.0.
name
Type: str
A human-readable name for the circuit.
cregs
Type: list[ClassicalRegister]
A list of the ClassicalRegisters in this circuit. You should not mutate this.
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